Volume 8, issue 3 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Moves and invariants for knotted handlebodies

Atsushi Ishii

Algebraic & Geometric Topology 8 (2008) 1403–1418
Abstract

We give fundamental moves for the neighborhood equivalence classes of spatial trivalent graphs. We define a coloring invariant and a cocycle invariant for the neighborhood equivalence classes and then for all spatial graphs. We show that the cocycle invariant detects the chirality of a knotted handlebody.

Keywords
knotted handlebody, spatial graph, coloring, cocycle invariant, chirality
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M15, 57M25
References
Publication
Received: 29 January 2008
Revised: 8 May 2008
Accepted: 13 June 2008
Published: 3 September 2008
Authors
Atsushi Ishii
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan