Reduced Polynomial of Framed Links in Thickened Torus
Received:January 17, 2017  Revised:October 28, 2017
Key Word: reduced polynomial   framed link   thickened torus   Kauffman bracket skein algebra  
Fund ProjectL:Supported by Guangdong Province Innovation Talent Project for Youths (Grant No.2015KQNCX107) and Guangdong University of Education Special Fund for Doctoral Research (Grant No.2016ARF06).
Author NameAffiliation
Xinming YAN Department of Mathematics, Guangdong University of Education, Guangdong 510303, P. R. China 
Meng SUN The China-Russian Joint Training Graduate School, Heilongjiang University, Heilongjiang 150080, P. R. China 
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      Framed links in thickened torus is studied. We give an expression of torus knot in the Kauffman bracket skein algebra. From this expression and using the theory of Gr\"{o}bner bases, we drive the reduced polynomial of a framed link, which is an ambient isotopic invariant and can be computed feasibly.
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