Artin presentations, triangle groups, and 4-manifolds
Geometric Topology
2021-07-26 v2
Abstract
Gonz{\'a}lez-Acu{\~n}a showed that Artin presentations characterize closed, orientable -manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smooth, compact, simply-connected -manifold. We utilize triangle groups to find all Artin presentations on two generators that present the trivial group. We then determine all smooth, closed, simply-connected -manifolds with second betti number at most two that appear in Artin presentation theory.
Keywords
Cite
@article{arxiv.2010.08383,
title = {Artin presentations, triangle groups, and 4-manifolds},
author = {Jack S. Calcut and Jun Li},
journal= {arXiv preprint arXiv:2010.08383},
year = {2021}
}
Comments
13 pages, 10 figures. Included a proof of the folklore Theorem 2.11 (at the request of a referee), included more examples in Section 2, and made a few minor changes