The Kauffman bracket skein module of \(S^ 1\times S^ 2\)
type: Item
instance of: scholarly article
title: The Kauffman bracket skein module of \(S^ 1\times S^ 2\)
zbMATH Open document ID: 0826.57007
DOI: 10.1007/BF02572603
author: Jim Hoste
author: Józef H. Przytycki
published in: Mathematische Zeitschrift
publication date: 1995-12-05T00:00:00Z
full work available at URL: https://eudml.org/doc/174798
review text: We compute the skein module \({\mathcal S} (S^1\times S^2)\). This module over the ring \(R= \mathbb{Z} [A^{\pm 1}]\) generalizes the Jones polynomial to links in \(S^1\times S^2\). The definition of \({\mathcal S} (S^1\times S^2)\) rests squarely on Kauffman's approach to the Jones polynomial via his bracket polynomial. In particular we obtain Theorem: The skein module of \(S^1\times S^2\) is \[ {\mathcal S} (S^1\times S^2) \cong R\oplus \bigoplus ^\infty_{i=1} R/(1- A^{2i+4}). \]
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 799548
zbMATH Keywords: skein module \({\mathcal S} (S^ 1\times S^ 2)\)
zbMATH Keywords: links in \(S^ 1\times S^ 2\)
zbMATH Keywords: bracket polynomial
zbMATH Keywords: skein module of \(S^ 1\times S^ 2\)
MaRDI profile type: Publication
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OpenAlex ID: W2041488616
description: scientific article; zbMATH DE number 799548