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

2011/06/23 by Yuya Koda, Koda, Yuya · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #20F05 #57M15 #57M25 #Advanced Materials and Mechanics #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1106.4777

openalex publication_date 2011/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Automorphisms of the 3-sphere that preserve a genus two Heegaard splitting
• A TABLE OF GENUS TWO HANDLEBODY-KNOTS UP TO SIX CROSSINGS

Cited by

• Handlebody-knots obtained by tangle replacement
• On symmetry and exterior problems of knotted handlebodies

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• A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting
• Topological symmetry groups and mapping class groups for spatial graphs
• Spaces of Knots
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• The sphere complex of a locally finite graph