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Rational homology of spaces of complex monic polynomials with multiple roots

Part of: Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  26 February 2010

Dmitry N. Kozlov
Dmitry N. Kozlov
Affiliation:
Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, U.S.A.
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Abstract

This paper treats rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements reduces the problem to studying certain triangulated spaces Xλ,μ.

MSC classification

Secondary: 58K15: Topological properties of mappings
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 77 - 91
Copyright
Copyright © University College London 2002

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References

1.Arnold, V. I.. The cohomology ring of the group of dyed braids. Mat. Zametki, 5 (1969). 227–231(Russian).Google Scholar
2.Arnold, V. I.. On some topological invariants of algebraic functions. Trans. Moscow Math. Soc., 21 (1970), 30–52.Google Scholar
3.Arnold, V. I.. On some topological invariants of algebraic functions, II. Func. Anal. Pril., 4 (1970), l–9(Russian).Google Scholar
4.Babson, E., Björner, A., Linusson, S., Shareshian, J. and Welker, V.. Complexes of not i-connected graphs. Topology, 38 (1999), 271–299.CrossRefGoogle Scholar
5.Björner, A.. Subspace arrangements, in “First European Congress of Mathematics, Paris 1992” (eds. Joseph, A.et al), Progress in Math., 119 (Birkhäuser, 1994), 321–370.Google Scholar
6.Bredon, G. E.. Introduction to Compact Transformation Groups (Academic Press, 1972).Google Scholar
7.Conner, P. E.. Concerning the action of a finite group. Proc. Nat. Acad. Sci. U.S.A., 142 (1956), 349–351.CrossRefGoogle Scholar
8.Fulton, W. and MacPherson, R.. A compactification of configuration spaces. Ann. of Math., 139 (1994), 183–225.CrossRefGoogle Scholar
9.Forman, R.. Morse theory for cell complexes. Adv. Math., 134 (1998), 90–145.CrossRefGoogle Scholar
10.Fuchs, D. B.. Cohomology of braid group mod 2. Func. Anal. Pril., 4 (1970), 62–75.(Russian).Google Scholar
11.Gelfand, S. and Manin, Y.. Methods of Homological Algebra (Translated from the 1988 Russian original). (Springer, Berlin, 1996).CrossRefGoogle Scholar
12.Hanlon, P.. A proof of a conjecture of Stanley concerning partitions of a set. European J. Combin., 4 (1983), 137–141.CrossRefGoogle Scholar
13.Knudsen, F.. Projectivity of the moduli space of stable curves, II: the stacks Mg, n. Math. Scand., 52 (1983), 1225–1265.Google Scholar
14.Kozlov, D. N.. General lexicographic shellability and orbit arrangements. Ann. of Comb., 1 (1997), 67–90.CrossRefGoogle Scholar
15.Kozlov, D. N.. Collapsibility of Δ(Πn)/fn and some related CW complexes. Proc. A.M.S. 128 (2000), 2253–2259.CrossRefGoogle Scholar
16.Shapiro, B. and Welker, V.. Combinatorics and topology of stratifications of the space of monic polynomials with real coefficients. Result. Math., 33 (1998), 338–355.CrossRefGoogle Scholar
17.Stanley, R. P.. Some aspects of groups acting on finite posets. J. Combin. Theory Ser. A, 32 (1982), 132–161.CrossRefGoogle Scholar
18.Sundaram, S. and Welker, V.. Group actions on arrangements of linear subspaces and applications to configuration spaces. Trans. Amer. Math. Soc., 349 (1997), 1389–1420.CrossRefGoogle Scholar
19.Vainshtain, F. V.. Cohomology of the braid groups. Func. Anal. Appl., 12 (1978), 135–137.CrossRefGoogle Scholar
20.Vassiliev, V. A.. Complements of Discriminants of Smooth Maps: Topology and Applications. AMS Transl. of Math. Monographs, 98 (Providence, RI, 1994).Google Scholar
21.Kozlov, D. N.. Topology of spaces of hyperbolic polynomials and combinatorics of resonances. Israel J. Math. 132 (2002), 189–206.CrossRefGoogle Scholar