Nine generators of the skein space of the 3–torus

Carrega, Alessio

doi:10.2140/agt.2017.17.3449

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

Alessio Carrega

Algebraic & Geometric Topology 17 (2017) 3449–3460

DOI: 10.2140/agt.2017.17.3449

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

Mathematical Subject Classification 2010

Primary: 57MXX

References

Publication

Received: 28 April 2016

Revised: 8 April 2017

Accepted: 28 April 2017

Published: 4 October 2017

Authors

Alessio Carrega
Dipartimento di Matematica “Tonelli” Università di Pisa Pisa Italy

Volume 17, issue 6 (2017)