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Local structure of some Out(Fn)-complexes

Published online by Cambridge University Press:  20 January 2009

Karen Vogtmann
Karen Vogtmann
Affiliation:
Cornell UniversityIthaca, New York 14853, U.S.A.
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Abstract

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In previous work of the author and M. Culler, contractible simplicial complexes were constructed on which the group of outer automorphisms of a free group of finite rank acts with finite stabilizers and finite quotient. In this paper, it is shown that these complexes are Cohen-Macauley, a property they share with buildings. In particular, the link of a vertex in these complexes is homotopy equivalent to a wedge of spheres of codimension 1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 3 , October 1990 , pp. 367 - 379
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Culler, M. and Vogtmann, K., Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986), 91–119.CrossRefGoogle Scholar
2.Quillen, D., Homotopy properties of the poset of p-subgroups of a finite group, Adv. in Math. 28 (1978), 129–137.CrossRefGoogle Scholar