Extending free group action on surfaces

Jesus Emilio Dominguez; Carlos Segovia

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arXiv · 2012.02464

Extending free group action on surfaces

Jesus Emilio Dominguez·Carlos Segovia

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Abstract

The present work introduces new perspectives in order to extend finite group actions from surfaces to 3-manifolds. We consider the Schur multiplier associated to a finite group $G$ in terms of principal $G$-bordisms in dimension two, called $G$-cobordisms. We are interested in the question of when a free action of a finite group on a closed oriented surface extends to a non-necessarily free action on a 3-manifold. We show the answer to this question is affirmative for abelian, dihedral, symmetric and alternating groups. As an application of our methods, we show that every non-necessarily free action of abelian groups (under certain conditions) and dihedral groups on a closed oriented surface extends to $3$-dimensional handlebody.

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Jesus Emilio Dominguez, Carlos Segovia. 2020-12-04. Extending free group action on surfaces. https://arxiv.org/abs/2012.02464

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