Let denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on which is quadratic in g. For the proofs we develop a calculus for finite group actions on , by codifying such actions by handle-orbifolds and finite graphs of finite groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-3,
author = {Bruno P. Zimmermann},
title = {On finite groups acting on a connected sum of 3-manifolds S$^2$ $\times$ S$^1$},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {131-142},
zbl = {1304.57026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-3}
}
Bruno P. Zimmermann. On finite groups acting on a connected sum of 3-manifolds S² × S¹. Fundamenta Mathematicae, Tome 227 (2014) pp. 131-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm226-2-3/