Ebook: Homological Stability for Automorphism Groups

New York.: Ithaca. Cornell University Library, Sep. 12, 2014, p.p.: 1-46, English.
{Free Published: E-Print Cornell University Library (arXiv:1409.3541v1 [math.AT] 11 Sep 2014)}.
Abstract.
We prove a general homological stability theorem for families of automorphism groups in certain categories.
We show that this theorem can be applied to all the classical examples of stable families of groups, such as the symmetric groups, general linear groups and mapping class groups, and obtain new stability theorems with twisted coecients for the braid groups, automorphisms of free groups, mapping class groups of non-orientable surfaces and mapping class groups of 3{manifolds.Contents.
Introduction.
Homogenous categories.
Simplicial complexes and semi-simplicial sets.
Homological stability with constant coecients.
Stability with twisted coecients, qualitative version.
Quantitative stability with twisted coecients.
Examples.
Appendix: Properties of the simplicial complexes Sn(X; A).
References.