2020/12/04 by Dominguez, Jesus Emilio, Segovia, Carlos
#57M60 (Primary) #57R85 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2012.02464
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.