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On the first end invariant of an exact sequence

Published online by Cambridge University Press:  26 February 2010

F. E. A. Johnson
Affiliation:
Department of Mathematics, University College, London.. Gower Street, London WCIE 6BT.
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Extract

The notion of stability at infinity for an infinite finitely presented group with one end was introduced in [14], and for groups stable at infinity, the end invariant e was defined and studied for some (non-trivial) direct products. In this paper we study the corresponding problem for extensions.

Type
Research Article
Copyright
Copyright © University College London 1975

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References

1. Barratt, M. G., Gugenheim, V. K. A. M. and Moore, J. C.. “On semisimplicial fibre bundles”, Amer. J. Math., 81 (1959), 639657.CrossRefGoogle Scholar
2. Bieri, R. and Eckmann, B.. “Groups with homological duality generalizing Poincaré duality”, Invent. Math., 20 (1973), 103124.CrossRefGoogle Scholar
3. Borel, A.. “On the automorphisms of certain subgroups of semisimple Lie groups”, Algebraic Geometry, Bombay Colloquium, (Oxford University Press, 1969), 4373.Google Scholar
4. Borel, A.. Linear Algebraic Groups. (Benjamin, 1969).Google Scholar
5. Borel, A. and , Harish-Chandra. “Arithmetic Subgroups of Algebraic Groups”, Ann. of. Math. (2), 75 (1962), 485535.CrossRefGoogle Scholar
6. Borel, A. and Serre, J. P.. “Corners and Arithmetic group”, Comment. Math. Helv., 48 (1974), 244297.Google Scholar
7. Borel, A. and Serre, J. P.. “Cohomologie d'immeubles et de groupes S-arithmetiques ' (to appear).Google Scholar
8. Brown, K., (to appear)Google Scholar
9. Chapman, T. A.. “Triangulation Theorem for Hilbert cube manifolds”. (to appear).Google Scholar
10. Chapman, T. A.. “Topological Invariance of Whitehead Torsion”. (to appear).Google Scholar
11. Farrell, F. T.. Thesis (Yale University, 1967).Google Scholar
12. Gabriel, P. and Zisman, M.. Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik, 35, (Springer-Verlag, 1967).CrossRefGoogle Scholar
13. Gruenberg, K.. “The hypercentre of linear groups”, j. Algebra, 8 (1968), 3440.CrossRefGoogle Scholar
14. Johnson, F. E. A.. “Manifolds of homotopy type K(π, 1) II”. Proc. Camb. Phil. Soc, 75 (1974), 165173.CrossRefGoogle Scholar
15. Johnson, F. E. A.. “On a conjecture of Wall, C. T. C., (to appear).Google Scholar
16. Johnson, F. E. A.. “The end behaviour of some finitely presented groups”, (to appear).Google Scholar
17. Lee, R. and Raymond, F.. “Aspherical manifolds”, (to appear).Google Scholar
18. Maclane, S.. Homology (Springer-Verlag, 1963).CrossRefGoogle Scholar
19. Mal'cev, A. I.. “On a class of homogeneous spaces”. Amer. Math. Soc. Transl., No. 39. (1951).Google Scholar
20. Makarov, V. S.. “On a certain class of discrete groups of Lobač evskii space having an infinite fundamental region of finite measure”. Soviet. Math. Dokl., 7, (1966), 328331.Google Scholar
21. May, J. P.. Simplicial objects in Algebraic Topology (Van Nostrand, 1967).Google Scholar
22. Mostow, G. D.. Strong Rigidity of Locally Symmetric Spaces, Annals of Mathematics Studies, No. 78 (Princeton, 1973).Google Scholar
23. Neumann, H.. Varieties of Groups, Ergebnisse der Mathematik, No. 37, (Springer-Verlag, 1966).Google Scholar
24. Neuwirth, L.. Knot Groups, Annals of Mathematics Studies. No. 56 (Princeton, 1965).CrossRefGoogle Scholar
25. Nielsen, J.. 'Untersuchungen zur Topologie der geschlossenen Zweiseitigen Flähen”, Ada Math., 50 (1927), 266.Google Scholar
26. Raghunathan, M. S.. Discrete Subgroups of Lie groups, Ergebnisse der Mathematik, No. 68, (Springer-Verlag, 1972).CrossRefGoogle Scholar
27. Remeslennikov, V. N.. “Finitely presented groups”, Fourth All Union symposium on the theory of groups, Novosibirsk, 1973, p. 164169.Google Scholar
28. Serre, J. P.. Cohomologie des groupes discrets, Prospects in Mathematics, Annals of Mathematics Studies, No. 70 (Princeton, 1971), 77169.Google Scholar
29. Siebenmann, L. C.. “A Total Whitehead Obstruction to fibering over a circle”, Comment. Math. Helv., 45 (1970), 148.CrossRefGoogle Scholar
30. Stallings, J.. “On fibering certain 3-manifolds”, Topology of 3-manifolds and Related Topics (Prentice-Hall, 1962).Google Scholar
31. Stallings, J.. “The piecewise-linear structure of Euclidean Space”, Proc. Camb. Phil. Soc, 58 (1962), 481–88.CrossRefGoogle Scholar
32. Stallings, J.. “The Whitehead group of free products”, Ann. of Math., 82 (1965), 354363.CrossRefGoogle Scholar
33. Stallings, J.. Embedding homotopy types into manifolds, Princeton University mimeographed notes (Princeton, 1965).Google Scholar
34. Stallings, J.. “Torsion free groups with infinitely many ends”, Ann. of Math., 88 (1968), 312334.CrossRefGoogle Scholar
35. Stallings, J.. Group Theory and three dimensional manifolds (Yale University, 1972).Google Scholar
36. Vinberg, E. B.. “Discrete groups generated by reflections in Lobačevskii space“, Math. Sbornik, 72. (1967), 471–88.Google Scholar
37. Waldhausen, F.. “On irreducible 3-manifolds which are sufficiently large”, Ann. of. Math., 87 (1968), 5688.CrossRefGoogle Scholar
38. Waldhausen, F.. Whitehead groups of generalised free products, Notes. (Bochum University, 1969).Google Scholar
39. Wall, C. T. C.. “Finiteness Conditions for C. W. complexes”, Ann. of. Math., 81 (1965), 5669.CrossRefGoogle Scholar
40. Wall, C. T. C.. “Finiteness Conditions for C.W. complexes II”, Proc. Roy. Soc, Ser A., 295 (1966), 129139.Google Scholar
41. Wehrfritz, B. A. F.. Infinite Linear Groups, Ergebnisse der Mathematik, No. 76 (Springer-Verlag, 1973).CrossRefGoogle Scholar
42. West, J. E.. “Mapping cylinders of Hilbert Cube factors”, Gen. Top. App., 1 (1971), 111125.CrossRefGoogle Scholar
43. Zassenhaus, H.. “Beweis eines Satzes uber diskrete Gruppen”, Abh. Math. Sem. Univ. Hamburg 12 (1938), 289312.CrossRefGoogle Scholar