One-relator groups and proper 3-realizability
Abstract
How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group is said to be properly 3-realizable if there exists a compact 2-polyhedron with whose universal cover has the proper homotopy type of a PL 3-manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated one-relator groups and show that those having finitely many ends are properly 3-realizable, by describing what the fundamental pro-group looks like, showing a property of one-relator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that one-relator groups are semistable at infinity.
Cite
@article{arxiv.0910.0305,
title = {One-relator groups and proper 3-realizability},
author = {M. Cárdenas and F. F. Lasheras and A. Quintero and D. Repovš},
journal= {arXiv preprint arXiv:0910.0305},
year = {2009}
}