Artin presentations, triangle groups, and 4-manifolds

Jack S. Calcut; Jun Li

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arXiv · 2010.08383

Artin presentations, triangle groups, and 4-manifolds

Jack S. Calcut·Jun Li

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Abstract

Gonz{\'a}lez-Acu{\~n}a 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.

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Jack S. Calcut, Jun Li. 2020-10-16. Artin presentations, triangle groups, and 4-manifolds. https://arxiv.org/abs/2010.08383

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