New York Journal of Mathematics
Volume 24 (2018), 661-688


Mohamed Imad Bakhira and Benjamin Cooper

Gradation of Algebras of Curves by the Winding Number

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Published: September 13, 2018
Keywords: Goldman Lie algebra, winding number, HOMFLY-PT skein, grading.
Subject: 16T99, 53D99, 81R50.

We construct a new grading on the Goldman Lie algebra of a closed oriented surface by the winding number. This grading induces a grading on the HOMFLY-PT skein algebra and related algebras. Our work supports the conjectures of B. Cooper and P. Samuelson in their paper "The Hall algebras of surfaces I".


The second author would like to thank P. Samuelson for the friendly conversations and suggestions. Both authors would like to thank C. Frohman and J. Greene, as well as the referee for the careful reading.

Author information

Mohamed Imad Bakhira:
Department of Mathematics,University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA.

Benjamin Cooper:
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA.