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

Bruno P. Zimmermann

Fundamenta Mathematicae (2014)

  • Volume: 226, Issue: 2, page 131-142
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Bruno P. Zimmermann. "On finite groups acting on a connected sum of 3-manifolds S² × S¹." Fundamenta Mathematicae 226.2 (2014): 131-142. <http://eudml.org/doc/286137>.

@article{BrunoP2014,
abstract = {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.},
author = {Bruno P. Zimmermann},
journal = {Fundamenta Mathematicae},
keywords = {closed handle; bound on finite group action},
language = {eng},
number = {2},
pages = {131-142},
title = {On finite groups acting on a connected sum of 3-manifolds S² × S¹},
url = {http://eudml.org/doc/286137},
volume = {226},
year = {2014},
}

TY - JOUR
AU - Bruno P. Zimmermann
TI - On finite groups acting on a connected sum of 3-manifolds S² × S¹
JO - Fundamenta Mathematicae
PY - 2014
VL - 226
IS - 2
SP - 131
EP - 142
AB - 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.
LA - eng
KW - closed handle; bound on finite group action
UR - http://eudml.org/doc/286137
ER -

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