Gradation of Algebras of Curves by the Winding Number
Mohamed Imad Bakhira, Benjamin Cooper
TL;DR
This paper introduces a novel grading based on winding numbers for the Goldman Lie algebra of surfaces, which extends to related skein algebras, providing new insights into their algebraic structure.
Contribution
It constructs a new winding number-based grading on the Goldman Lie algebra and extends this to HOMFLY-PT skein and related algebras, supporting existing conjectures.
Findings
New grading on Goldman Lie algebra
Extension of grading to skein algebras
Supports conjectures of Cooper and Samuelson
Abstract
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
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology