Title

Artin presentations, triangle groups, and 4-manifolds

Abstract

Gonzalez-Acuna 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.

Publisher

Springer

Publication Date

3-25-2022

Publication Title

Boletin De La Sociedad Matematica Mexicana

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1007/s40590-022-00423-w

Keywords

Artin presentation, Pure braid, Fundamental group, 3-manifold, 4-manifold, Triangle group, Mapping class group

Language

English

Format

text

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