The total Johnson homomorphism on the homology cylinder and the bracket-quantization HOMFLY-PT skein algebra
Shunsuke Tsuji
TL;DR
This paper introduces a new method to compute automorphisms induced by homology cylinders using Goldman Lie algebra and skein algebra, refining existing formulas and advancing understanding of surface automorphisms.
Contribution
It presents a novel approach to calculating automorphisms via Goldman Lie algebra and skein algebra, refining previous formulas by Kuno and Massuyeau.
Findings
New computational method for automorphisms of homology cylinders
Refinement of Kuno and Massuyeau's formula
Enhanced understanding of the algebraic structures involved
Abstract
A homology cylinder of a surface induces an automorphism of the completed group ring of the fundamental group of the surface. We introduce a new method of computing the automorphism by using the Goldman Lie algebra of the surface or some skein algebra. In particular, we give a refinement of a formula by Kuno and Massuyeau.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models