 

Charles Frohman,
Joanna KaniaBartoszynska, and
Thang Le
Skein algebras of threemanifolds at 4th roots of unity
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Published: 
October 27, 2023. 
Keywords: 
Skein algebras, Kauffman bracket, quantum topology. 
Subject [2010]: 
57K31. 


Abstract
This paper introduces an algebra structure on the part of the skein module of an arbitrary 3manifold M spanned by links that represent 0 in H_{1}(M;Z_{2}) when the value of the parameter used in the Kauffman bracket skein relation is equal to ± i. It is proved that if M has no 2torsion in H_{1}(M;Z) then those algebras, K_{± i}^{0}(M), are naturally isomorphic to the corresponding algebras when the value of the parameter is ± 1. This implies that the algebra K_{± i}^{0}(M) is the unreduced coordinate ring of the variety of PSL_{2}(C)characters of π_{1}(M) that lift to SL_{2}(C)representations.


Acknowledgements
This material is based upon work supported by and while serving at the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.


Author information
Charles Frohman
Department of Mathematics
The University of Iowa
Iowa City, IA 52242, USA
charlesfrohman@uiowa.edu
Joanna KaniaBartoszynska
National Science Foundation
Arlington, VA, 22230, USA
jkaniaba@nsf.gov
Thang Le
School of Mathematics
Geogia Institute of Technology
686 Cherry St NW, Atlanta, GA 30332, USA
letu@math.gatech.edu

