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A NOTE ON THE SHADOW COCYCLE INVARIANT OF A KNOT WITH A BASE POINT

S. SATOH

Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

https://doi.org/10.1142/S0218216507005579Cited by:6 (Source: Crossref)

Abstract

Fox's shadow p-colorings of a knot K define two kinds of Laurent polynomials, Φ_p(K) and , as invariants of K. We prove that the equality holds for any knot K. Also we prove that, if the p-coloring number of K is equal to p², then has the form for some N ∈ ℤ_p.

Dedicated to Professor Louis H. Kauffman for his 60th birthday

Keywords:

AMSC: 57M25, 57M27

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