A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds
Group Theory
2016-01-20 v3
Abstract
We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus theorem, is derived using Cappell's surgery methods from a new algebraic splitting theorem for Poincare duality groups. As an application we derive a new obstruction to the existence of \pi_1-injective maps.
Keywords
Cite
@article{arxiv.1110.2041,
title = {A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds},
author = {Aditi Kar and Graham A. Niblo},
journal= {arXiv preprint arXiv:1110.2041},
year = {2016}
}
Comments
This is the final version of our article `Topological Superrigidity'