Artin presentations, triangle groups, and 4-manifolds
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.
Calcut, Jack S. 2022. "Artin presentations, triangle groups, and 4-manifolds." Boletin de la Sociedad Matematica Mexicana 28(2): 27.
Boletin De La Sociedad Matematica Mexicana
Artin presentation, Pure braid, Fundamental group, 3-manifold, 4-manifold, Triangle group, Mapping class group