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# Quandle Cocycle Invariants for Spatial Graphs and Knotted Handlebodies

Published:2011-06-25
Printed: Feb 2012
• Atsushi Ishii,
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
• Masahide Iwakiri,
Osaka City University Advanced Mathematical Institute, 3-3-138, Sugimoto, Sumiyoshi-ku Osaka, 558-8585, Japan
 Format: LaTeX MathJax

## Abstract

We introduce a flow of a spatial graph and see how invariants for spatial graphs and handlebody-links are derived from those for flowed spatial graphs. We define a new quandle (co)homology by introducing a subcomplex of the rack chain complex. Then we define quandle colorings and quandle cocycle invariants for spatial graphs and handlebody-links.
 Keywords: quandle cocycle invariant, knotted handlebody, spatial graph
 MSC Classifications: 57M27 - Invariants of knots and 3-manifolds 57M15 - Relations with graph theory [See also 05Cxx] 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}

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