Volume 17, issue 6 (2017)

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Nine generators of the skein space of the $3$–torus

Alessio Carrega

Algebraic & Geometric Topology 17 (2017) 3449–3460
Abstract

We show that the skein vector space of the $3$–torus is finitely generated. We show that it is generated by nine elements: the empty set, some simple closed curves representing the nonzero elements of the first homology group with coefficients in  ${ℤ}_{2}$, and a link consisting of two parallel copies of one of the previous nonempty knots.

Keywords
skein space, skein module, Kauffman bracket, Jones polynomial, 3-torus
Primary: 57MXX
Publication
Revised: 8 April 2017
Accepted: 28 April 2017
Published: 4 October 2017
Authors
 Alessio Carrega Dipartimento di Matematica “Tonelli” Università di Pisa Pisa Italy