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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2014 | 226 | 2 | 131-142

## On finite groups acting on a connected sum of 3-manifolds S² × S¹

EN

### Abstrakty

EN
Let $H_{g}$ 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 $H_{g}$ 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 $H_{g}$ which is quadratic in g. For the proofs we develop a calculus for finite group actions on $H_{g}$, by codifying such actions by handle-orbifolds and finite graphs of finite groups.

131-142

wydano
2014

### Twórcy

autor
• Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, 34127 Trieste, Italy