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

• Autorzy: Bruno P. Zimmermann
• Języki publikacji: 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.

Kategorie tematyczne

• 57S25: Groups acting on specific manifolds
• 57M60: Group actions in low dimensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 226
• Numer: 2
• Strony: 131-142

Daty

wydano

2014

Twórcy

autor

Bruno P. Zimmermann

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

Identyfikatory

DOI

10.4064/fm226-2-3