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.
Repository Citation
Calcut, Jack S. 2022. "Artin presentations, triangle groups, and 4-manifolds." Boletin de la Sociedad Matematica Mexicana 28(2): 27.
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
