English

Alexander varieties and largeness of finitely presented groups

Group Theory 2012-05-02 v1 Geometric Topology

Abstract

Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)\geq N. We give some applications of this result to the study of hyperbolic 3--manifolds, mapping classes of surfaces and combinatorial group theory.

Keywords

Cite

@article{arxiv.1205.0184,
  title  = {Alexander varieties and largeness of finitely presented groups},
  author = {Thomas Koberda},
  journal= {arXiv preprint arXiv:1205.0184},
  year   = {2012}
}

Comments

This article is essentially part two of the author's thesis