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Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots

Published online by Cambridge University Press:  03 February 2015

YUYA KODA
YUYA KODA*
Affiliation:
Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan. e-mail: ykoda@hiroshima-u.ac.jp
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Abstract

We consider the group of isotopy classes of automorphisms of the 3-sphere that preserve a spatial graph or a handlebody-knot embedded in it. We prove that the group is finitely presented for an arbitrary spatial graph or a reducible handlebody-knot of genus two. We also prove that the groups for “most” irreducible genus two handlebody-knots are finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 1 , July 2015 , pp. 1 - 22
Copyright
Copyright © Cambridge Philosophical Society 2015 

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