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- Title
ON NORMALIZATIONS OF A REGULAR ISOTOPY INVARIANT FOR SPATIAL GRAPHS.
- Authors
ISHII, ATSUSHI
- Abstract
We give a framework to normalize a regular isotopy invariant of a spatial graph, and introduce many normalizations satisfying the same relation under a local move. We normalize the Yamada polynomial for spatial embeddings of almost all trivalent graphs without a bridge, and see the benefit to utilize our normalizations from the viewpoint of skein relations, the finite type invariants, and evaluations of the Yamada polynomial. We show that the collection of the differences between two of our normalizations is a complete spatial-graph-homology invariant.
- Subjects
INVARIANTS (Mathematics); GRAPH theory; POLYNOMIALS; HOMOLOGY theory; COMPLETE graphs; MATHEMATICAL analysis
- Publication
International Journal of Mathematics, 2011, Vol 22, Issue 11, p1545
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X1100729X