Symmetric automorphisms of free products

Memoirs of the American Mathematical Society

Volumn , Issue 582, 1996, Pages 1-97

  McCullough, Darryl ^a   Miller, Andy ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Automorphism; Cohomological dimension; Contractible complex; Euler characteristic; FL; Free product; R tree; Symmetric automorphism; Torsion; Virtual cohomological dimension; Whitehead automorphism

Indexed keywords

EID: 0030186686     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0582     Document Type: Article

References (36)

1. [B1] R. Bieri, Homological Dimension of Discrete Groups, Queen Mary College Mathematics Notes, London, 1976.
2. [B2] E. Bloomberg, Manifolds with no periodic homeomorphisms, Trans. Amer. Math. Soc. 202 (1975), 67-78.
3. [B3] K. Brown, Cohomology of Groups, Springer-Verlag Graduate Texts in Mathematics Vol. 87, New York, 1982.
4. [B4] K. Brown, Presentations for groups acting on simply-connected complexes, J. Pure and Applied Algebra 32 (1984), 1-10.
5. [BS] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comm. Math. Helv. 48 (1973), 436-491.
6. [C1] D. Collins, The automorphism group of a free product of finite groups, Arch. der Math. 50 (1988), 385-390.
7. [C2] D. Collins, Cohomological dimension and symmetric automorphisms of a free group, Comment. Math. Helvetici 64 (1989), 44-61.
8. [CG] D. Collins and N. Gilbert, Structure and torsion in automorphism groups of free products, Quart. J. Math. 41 (1990), 155-178.
9. [CZ] D. Collins and H. Zieschang, Rescuing the Whitehead method for free products I: Peak reduction, Math. Z. 185 (1984), 487-504.
10. [CM] M. Culler and J. Morgan, Group actions on IR-trees, Proc. London Math. Soc. 55 (1987), 571-604.
11. [CV] M. Culler and K. Vogtmann, Moduli of graphs and outer automorphisms of free groups, Invent. Math. 84 (1986), 91-119.
12. [EG] S. Eilenberg and T. Ganea, On the Lusternik-Schnirelmann category of abstract groups, Ann. of Math. 65 (1957), 517-518.
13. [F-R1] D.I. Fouxe-Rabinovitch, On the automorphism group of free products I, Math. Sb. 8 (1940), 265-276.
14. [F-R2] D.I. Fouxe-Rabinovitch, On the automorphism group of free products II, Math. Sb. 9 (1941), 183-220.
15. [F] L. Fuchs, Infinite Abelian Groups, Volume I, Academic Press, New York, 1970.
16. [G] N. Gilbert, Presentations of the automorphism group of a free product, Proc. London Math. Soc. (3) 54 (1987), 115-140.
17. [H1] J. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986), 157-176.
18. [H2] W. Harvey, Boundary structures for the modular group, in Riemann Surfaces and Related Topics, Ann. of Math. Studies Vol. 97, Princeton University Press (1981), 245-251.
19. [HL] P. Higgins and R. Lyndon, Equivalence of elements under automorphisms of a free group, J. London Math. Soc. 8 (1974), 254-258.
20. [KV] S. Krstić and K. Vogtmann, Equivariant outer space and automorphisms of free-by-finite groups, Comment. Math. Helv. 68 (1993), 216-262.
21. [M1] J. McCool, The automorphism groups of finite extensions of free groups, Bull. London Math. Soc. 20 (1988), 131-135.
22. [M2] J. McCool, A presentation for the automorphism group of a free group of finite rank, J. London Math. Soc. 8 (1974), 259-266.
23. [M3] D. McCullough, Virtual cohomological dimension of mapping class groups of 3-manifolds, Bull. Amer. Math. Soc. 18 (1988), 27-30.
24. [M4] D. McCullough, Virtually geometrically finite mapping class groups of 3-manifolds, J. Diff. Geom. 33 (1991), 1-65.
25. [M5] G. Mostow, Strong Rigidity of Locally Symmetric Spaces, Ann. of Math. Studies, Vol. 78, Princeton University Press, Princeton, 1973.
26. [N] J. Nielsen, Die Isomorphismengruppe der freien gruppe, Math. Ann. 91 (1924), 169-209.
27. [P1] F. Paulin, The Gromov topology on IR-trees, Top. and its Appl. 32 (1989), 197-221.
28. [P2] F. Paulin, Outer automorphisms of hyperbolic groups and small actions on IR-trees, in Arboreal Group Theory, Math. Sci. Res. Inst. Publ. Vol. 19, Springer (1991), 331-343.
29. [Q] D. Quillen, Homotopy properties of the poset of nontrivial p-subgroups of a group, Adv. in Math. 28 (1978), 101-128.
30. [S1] H. Schneebeli, On virtual properties of group extensions, Math. Z. 159 (1978), 159-167.
31. [SW] G. P. Scott and C. T. C. Wall, Topological methods in group theory, in Homological Group Theory, London Math. Soc. Lecture Note Series Vol. 36 (1979), 137-203.
32. [S2] J.-P. Serre, Cohomologie des groupes discrets, Ann. of Math. Studies 70 (1971), 77-169.
33. [S3] J.-P. Serre, Trees, Springer-Verlag, Berlin, 1980.
34. [S4] R. Skora, Deformations of length functions in groups, preprint.
35. [S5] C. Soulé, Groupes opérant sur un complexe simplicial avec domaine fondamental, C. R. Acad. Sci. Paris sér. A 276 (1973), 607-609.
36. [W] J.H.C. Whitehead, On equivalent sets of elements in a free group, Ann. of Math. 37 (1936), 782-800.