2020/10/16 by Jack S. Calcut, Jun Li, Calcut, Jack S. +1
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:20F36 #msc:57K40 #msc:57M05
paper · pdf · doi:10.48550/arxiv.2010.08383
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
arxiv created 2021/07/22 · arxiv updated 2021/07/26
González-Acuña showed that Artin presentations characterize closed, orientable 3-manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smooth, compact, simply-connected 4-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 4-manifolds with second betti number at most two that appear in Artin presentation theory.