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Published online by Cambridge University Press:  16 December 2021

Christian Rosendal
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University of Maryland, Baltimore
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References

Abels, Herbert, Specker-Kompaktifizierungen von lokal kompakten topologischen Gruppen, Math.Z.,135 (1973/74), 325361.Google Scholar
Arens, Richard Friederich, Topologies for homeomorphism groups, Amer. J. Math., 68 (1946), 593610.Google Scholar
Bader, Uri and Rosendal, Christian, Coarse equivalence and topological couplings of locally compact groups, Geometriae Dedicata, 196 (2018), 19.Google Scholar
Bekka, Mohammed El Bachir, Chérix, Pierre-Alain and Valette, Alain, Proper Affine Isometric Actions of Amenable Groups, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (Oberwolfach, 1993), 1–4, London Mathematical Society Lecture Note Series 227 (Cambridge: Cambridge University Press, 1995).Google Scholar
Bekka, Mohammed El Bachir, Harpe, Pierre de la and Valette, Alain, Kazhdan’s Property (T), New Mathematical Monographs, 11 (Cambridge: Cambridge University Press, 2008).Google Scholar
Yaacov, Itaï Ben, Berenstein, Alexander, Henson, C. Ward and Usvyatsov, Alexander, Model theory for metric structures. In Chatzidakis, Z., Macpherson, D., Pillay, A. and Wilkie, A, eds., Model Theory with Applications to Algebra and Analysis, vol. 2, London Mathematical Society Lecture Note Series, 350 (Cambridge: Cambridge University Press, 2008), pp. 315427.Google Scholar
Yaacov, Itaï Ben, Melleray, Julien and Tsankov, Todor, Metrizable universal minimal flows of Polish groups have a comeagre orbit, Geom. Funct. Anal., 27(1) (2017), 6777.Google Scholar
Yaacov, Itaï Ben and Tsankov, Todor, Weakly almost periodic functions, model-theoretic stability, and minimality of topological groups, Trans. Amer. Math. Soc., 368(11) (2016), 82678294.Google Scholar
Benyamini, Yoav and Lindenstrauss, Joram, Geometric Nonlinear Functional Analysis, Volume 1 (Providence, RI: American Mathematical Society, 2000).Google Scholar
, George Mark Bergman, Generating infinite symmetric groups, Bull. London Math. Soc., 38 (2006), 429440.Google Scholar
Birkhoff, Garrett, A note on topological groups, Compositio Math., 3 (1936), 427430.Google Scholar
Block, Jonathan and Weinberger, Shmuel, Aperiodic tilings, positive scalar curvature and amenability of spaces,J.Amer.Math.Soc.,5 (1992), 907918.Google Scholar
Braga, Bruno de Mendonça, Topics in the nonlinear geometry of Banach spaces, Doctoral dissertation, University of Illinois at Chicago (2017).Google Scholar
Brown, Nathaniel and Guentner, Erik, Uniform embedding of bounded geometry spaces into reflexive Banach space, Proc. Amer. Math. Soc. 133(7) (2005), 20452050.Google Scholar
Peter, J. Cameron, Permutation Groups, London Mathematical Society Student Texts, 45 (Cambridge: Cambridge University Press, 1999).Google Scholar
Peter, J. Cameron and Anatoliĭ Moiseevich Vershik, Some isometry groups of the Urysohn space, Ann. Pure Appl. Logic, 143(13) (2006), 7078.Google Scholar
Chérix, Pierre-Alain, Cowling, Michael, Jolissant, Paul, Julg, Pierre and Valette, Alain, Groups with the Haagerup Property: Gromov’s a-T-menability (Basel: Birkhäuser, 2001).Google Scholar
Cherlin, Gregory, Homogeneous Ordered Graphs and Metrically Homogeneous Graphs, book in preparation.Google Scholar
Michael, P. Cohen, On the large scale geometry of diffeomorphism groups of 1-manifolds, Forum Mathematicum, 30(1) (2018), 7586.Google Scholar
Cornulier, Yves de, On lengths on semisimple groups, J. Topol. Anal., 1(2), (2009), 113121.CrossRefGoogle Scholar
Cornulier, Yves de, On the quasi-isometric classification of locally compact groups. In Caprace, P.-E. and Monod, N., eds., New Directions in Locally Compact Groups, London Mathematical Society Lecture Notes Series 447 (Cambridge: Cambridge University Press, 2018), pp. 275342.Google Scholar
Cornulier, Yves de and Harpe, Pierre de la, Metric Geometry of Locally Compact Groups, EMS Tracts in Mathematics, vol. 25 (European Mathematical Society, September 2016).Google Scholar
Cornulier, Yves de, Tessera, Romain and Valette, Alain, Isometric group actions on Hilbert spaces: growth of cocycles, Geom. Funct. Anal., 17 (2007), 770792.Google Scholar
Corson, Harry Herbert III and Klee Jr, Victor L., Topological classification of convex sets, Proc. Symp. Pure Math. VII, Convexity, Amer. Math. Soc. (1963), pp. 101181.Google Scholar
Dixmier, Jaques, Dual et quasidual d’une algèbre de Banach involutive, Trans. Amer. Math. Soc., 104 (1962), 278283.Google Scholar
Edwards, Robert D. and Kirby, Robion Cromwell, Deformations of spaces of imbeddings, Ann. Math. (2), 93 (1971), 6388.Google Scholar
Eliashberg, Yakov and Ratiu, Tudor Stefan, The diameter of the symplectomorphism group is infinite, Invent. Math., 103(2) (1991), 327340.Google Scholar
Ellis, Robert Mortimer, Universal minimal sets, Proc. Amer. Math. Soc., 11 (1960), 540543.Google Scholar
Eskin, Alex, Fisher, David and Whyte, Kevin, Coarse differentiation of quasi-isometries I: Spaces not quasi-isometric to Cayley graphs, Ann. Math., 176 (2012), 221260.Google Scholar
Fabian, Marián, Habala, Petr, Hájek, Petr, Santalucía, Vicente Montesinos and Zizler, Václav, Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC (New York: Springer, 2011).Google Scholar
Gordon, M. Fisher, On the group of all homeomorphisms of a manifold, Trans. Amer. Math. Soc., 97 (1960), 193212.Google Scholar
Følner, Erling, On groups with full Banach mean value, Math. Scand., 3 (1955), 243254.Google Scholar
Fraïssé, Roland, Sur l’extension aux relations de quelques proprietés des ordres, Ann. Sci. École Norm. Sup., 71 (1954), 363388.Google Scholar
John, M. Franks and Michael Handel, Distortion elements in group actions on surfaces, Duke Math. J., 131(3) (2006), 441468.Google Scholar
Gheysens, Maxime and Monod, Nicolas, Fixed points for bounded orbits in Hilbert spaces, Annales de l’ENS, 50(1) (2017), 131156.Google Scholar
Gromov, Mikhail Leonidovich, Asymptotic invariants of infinite groups. In Niblo, G. A. and Roller, M. A., eds., Geometric Group Theory, vol. 2 (Sussex, 1991), London Mathematical Society Lecture Note Series 182 (Cambridge: Cambridge University Press, 1993), pp. 1295.Google Scholar
Herbst, Manuel, 1-Cocycles of unitary representations of infinite-dimensional unitary groups, Doctoral dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg (2018).Google Scholar
Herndon, William Jake, Absolute continuity and large-scale geometry of Polish groups, arXiv: 1802.10239 (2018).Google Scholar
Herndon, Willian Jake, Deformations and Products of Polish Groups, Doctoral dissertation, University of Illinois at Chicago (2019).Google Scholar
Hopf, Heinz, Enden offener Räume und unendliche diskontinuierliche Gruppen, Comm. Math. Helv., 16 (1943/44), 81100.Google Scholar
Jaffard, Paul, Traité de topologie générale en vue de ses applications (Paris: Presses Universitaires de France, 1997).Google Scholar
Johnson, William Buhmann, Lindenstrauss, Joram and Schechtman, Gideon, Banach spaces determined by their uniform structure, Geom. Funct. Anal., 6 (1996), 430470.Google Scholar
Kakutani, Shizuo, Selected Papers, vol. 1. Edited and with a preface by Kallman, Robert R.. With a biographical sketch by Hajian, Arshag and Ito, Yuji. Contemporary Mathematicians (Boston, MA: Birkhäuser Boston, Inc., 1986).Google Scholar
Kakutani, Shizuo and Kodaira, Kunihiko, Über das Haarsche Mass in der lokal bikompakten Gruppe, Proc. Imp. Acad. Tokyo, 20 (1944), 444450. Selected Papers, vol. 1, Kallman, Robert R., ed. (Boston, MA: Birkhäuser Boston, Inc., 1986), pp. 6874.Google Scholar
Kalton, Nigel John, The non-linear geometry of Banach spaces, Rev. Mat. Comput., 21(1) (2008), 760.Google Scholar
Katětov, Miroslav, On universal metric spaces, General Topology and its Relations to Modern Analysis and Algebra, VI (Prague, 1986) (1988), 323330.Google Scholar
Kechris, Alexander Sotirios, Classical Descriptive Set Theory (New York: Springer Verlag, 1995).Google Scholar
Kechris, Alexander Sotirios, Pestov, Vladimir Germanovich and Todorčević, Stevo, Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups, Geom. Funct. Anal., 15(1) (2005), 106189.Google Scholar
Kechris, Alexander Sotirios and Rosendal, Christian, Turbulence, amalgamation and generic automorphisms of homogeneous structures, Proc. Lond. Math. Soc. (3), 94(2) (2007), 302350.Google Scholar
Klee Jr, Victor L., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc., 3 (1952) 484487.Google Scholar
Kolmogorov, Andrey Nikolaevich, Asymptotic characteristics of some completely bounded metric spaces, Dokl. Akad. Nauk SSSR, 108 (1956), 585589.Google Scholar
Kolmogorov, Andrey Nikolaevich and Tikhomirov, Vladimir Mikhaĭlovich, ɛ-entropy and ɛ-capacity of sets in function spaces, Uspehi Mat. Nauk, no. 2 (86), 14 (1959), 386; English translation, Amer. Math. Soc. Transl. (2), 17 (1961), 277364.Google Scholar
Krivine, Jean-Louis and Maurey, Bernard, Espaces de Banach stables, Israel J. Math., 39(4) (1981), 273295.Google Scholar
KuratowskiNardzewski, Kazimierz Czesław Ryll, A general theorem on selectors,Bull.Acad.Pol.Sci.Sér. Sci., Math., Astr. et Phys., 13 (1965), 397403.Google Scholar
Lusky, Wolfgang, The Gurarij spaces are unique, Arch. Math. (Basel), 27 (1976), 627635.Google Scholar
Mann, Kathryn, Automatic continuity for homeomorphism groups and applications. With an appendix on the structure of groups of germs of homeomorphism, written with Frederic Le Roux. Geometry & Topology, 20(5) (2016), 30333056.Google Scholar
Mann, Kathryn and Rosendal, Christian, Large scale geometry of homeomorphism groups, Ergod. Th. & Dynam. Sys., 38(7) (2018), 27482779.CrossRefGoogle Scholar
Marker, David Ellis, Model Theory: An Introduction (New York: Springer-Verlag, 2002).Google Scholar
Michael, G. Megrelishvili, Every semitopological semigroup compactification of the group H+[0,1] is trivial, Semigroup Forum, 63(3) (2001), 357370.Google Scholar
Meier, John, Groups, Graphs and Trees: An Introduction to the Theory of Infinite Groups, London Math. Soc. Student Texts 73 (Cambridge: Cambridge University Press, 2008).Google Scholar
Melleray, Julien, Topology of the Isometry group of the Urysohn space, Fundamenta Mathematicae, 207(3) (2010), 273287.Google Scholar
Militon, Emmanuel, Distortion elements for surface homeomorphisms, Geometry & Topology, 18 (2014), 521614.Google Scholar
Militon, Emmanuel, Conjugacy class of homeomorphisms and distortion elements in groups of homeomorphisms, Journal de l’École Polytechnique, 5 (2018), 565604.Google Scholar
Milnor, John, A note on curvature and fundamental group, J. Diff. Geom., 2 (1968), 17.Google Scholar
Mycielski, Jan, Independent sets in topological algebras, Fund. Math., 55 (1964), 139147.Google Scholar
Naor, Assaf, Uniform nonextendability from nets, C. R. Math. Acad. Sci. Paris, 353(11) (2015), 991994.Google Scholar
Nicas, Andrew and Rosenthal, David, Coarse structures on groups (English summary), Topology Appl., 159(14) (2012), 32153228.Google Scholar
Nowak, Piotr W. and Yu, Guoliang, Large Scale Geometry, EMS Textbooks in Mathematics (Zürich: European Mathematical Society (EMS), 2012).Google Scholar
Ornstein, Donald Samuel and Weiss, Benjamin, Entropy and isomorphism theorems for actions of amenable groups, J. d’Analyse Mathématique, 48 (1987), 1141.Google Scholar
Vladimir Germanovich Pestov, , A theorem of Hrushovski–Solecki–Vershik applied to uniform and coarse embeddings of the Urysohn metric space, Topology Appl., 155(14) (2008), 15611575.Google Scholar
Pettis, Billy James, On continuity and openness of homomorphisms in topological groups, Ann. Math. (2), 52 (1950), 293308.Google Scholar
Polterovich, Leonid, Growth of maps, distortion in groups and symplectic geometry, Invent. Math., 150(3) (2002), 655686.Google Scholar
Ricard, Éric and Rosendal, Christian, On the algebraic structure of the unitary group, Collect. Math., 58(2) (2007), 181192.Google Scholar
Roe, John, Index Theory, Coarse Geometry, and Topology of Manifolds, CBMS Regional Conference Series in Mathematics, 90 (published for the Conference Board of the Mathematical Sciences, Washington, DC, by the American Mathematical Society, Providence, RI, 1996).Google Scholar
Roe, John, Lectures on Coarse Geometry, University Lecture Series, 31 (Providence, RI: American Mathematical Society, 2003).Google Scholar
Roelcke, Walter and Dierolf, Susanne, Uniform Structures on Topological Groups and Their Quotients (New York: McGraw-Hill, 1981).Google Scholar
Rosendal, Christian, A topological version of the Bergman property, Forum Mathematicum, 21(2) (2009), 299332.Google Scholar
Rosendal, Christian, Global and local boundedness of Polish groups, Indiana Univ. Math. J., 62(5) (2013), 16211678.Google Scholar
Rosendal, Christian, Large scale geometry of metrisable groups, arXiv: 1403.3106 (2014).Google Scholar
Rosendal, Christian, Equivariant geometry of Banach spaces and topological groups, Forum Math., Sigma, 5(e22) (2017), 62 pages.CrossRefGoogle Scholar
Rosendal, Christian, Lipschitz structure and minimal metrics on topological groups,Arkivför matematik, 56(1) (2018), 185206.Google Scholar
Schneider, Friedrich Martin and Thom, Andreas, On Følner sets in topological groups, Compositio Mathematica, 154(7) (2018), 13331361.Google Scholar
Schwarz, Albert Solomonovich, A volume invariant of coverings (Russian). Dokl. Akad. Nauk SSSR (N.S.), 105 (1955), 3234.Google Scholar
Raymond, A. Struble, Metrics in locally compact groups, Compositio Math., 28 (1974), 217222.Google Scholar
Szép, Jenő, Über die als Produkt zweier Untergruppen darstellbaren endlichen Gruppen (German), Comment. Math. Helv., 22 (1949), 3133.Google Scholar
Tent, Katrin and Ziegler, Martin, On the isometry group of the Urysohn space, J. Lond. Math. Soc. (2), 87 (2013), 289303.Google Scholar
Tessera, Romain, Large scale Sobolev inequalities on metric measure spaces and applications, Rev. Mat. Iberoamericana, 24(3) (2008), 825865.Google Scholar
Tessera, Romain and Valette, Alain, Locally compact groups with every isometric action bounded or proper, J. Topol. Anal., 12(02) (2020), 267292.Google Scholar
Tsankov, Todor Dimitrov, Unitary representations of oligomorphic groups, Geom. Funct. Anal., 22(2) (2012), 528555.Google Scholar
Urysohn, Pavel Samuilovich, Sur un espace métrique universel, Bull. Sci. Math., 51 (1927), 4364, 7490.Google Scholar
Uspenskiĭ, Vladimir Vladimirovich, A universal topological group with a countable base, Funct. Anal. Appl., 20 (1986), 160161.Google Scholar
Veech, William, Topological dynamics, Bull. Amer. Math. Soc, 83(5) (1977), 775830.Google Scholar
Weaver, Nik, Lipschitz Algebras (River Edge, NJ: World Scientific Publishing Co., Inc., 1999).Google Scholar
Weil, André, Sur les espaces à structure uniforme et sur la topologie générale, Act. Sci. Ind. 551 (Paris: Hermann, 1937).Google Scholar
Whyte, Kevin, Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture, Duke Math. J., 99 (1999), 93112.Google Scholar
Yosida, Kôsaku, Mean ergodic theorem in Banach spaces, Proc. Imp. Acad., 14(8) (1938), 292294.Google Scholar
Zappa, Guido, Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro (Italian), Atti Secondo Congresso Un. Mat. Ital., Bologna, 1940, pp. 119125. (Rome: Edizioni Cremonense, 1942).Google Scholar
Zielinski, Joseph, An automorphism group of an ω-stable structure that is not locally (OB), Math. Log. Q., 62(6) (2016), 547551.Google Scholar
Zielinski, Joseph, Locally Roelcke precompact groups, arXiv: 1806.03752 (2018).Google Scholar

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  • References
  • Christian Rosendal, University of Maryland, Baltimore
  • Book: Coarse Geometry of Topological Groups
  • Online publication: 16 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781108903547.0011
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  • References
  • Christian Rosendal, University of Maryland, Baltimore
  • Book: Coarse Geometry of Topological Groups
  • Online publication: 16 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781108903547.0011
Available formats
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  • References
  • Christian Rosendal, University of Maryland, Baltimore
  • Book: Coarse Geometry of Topological Groups
  • Online publication: 16 December 2021
  • Chapter DOI: https://doi.org/10.1017/9781108903547.0011
Available formats
×