Moves and invariants for knotted handlebodies

Ishii, Atsushi

doi:10.2140/agt.2008.8.1403

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Moves and invariants for knotted handlebodies

Atsushi Ishii

Algebraic & Geometric Topology 8 (2008) 1403–1418

DOI: 10.2140/agt.2008.8.1403

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

Volume 8, issue 3 (2008)