A Geometric Proof of a Faithful Linear-Categorical Surface Mapping Class Group Action
Kyler Siegel
TL;DR
This paper provides a combinatorial proof that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category, using polygon-based methods and foundational results from bordered Heegaard Floer homology.
Contribution
It introduces a new combinatorial proof of the faithfulness of the surface mapping class group action on a linear category, expanding understanding of surface symmetries.
Findings
Proved faithful action of the mapping class group on a linear category.
Developed combinatorial methods using polygons for the proof.
Established foundational results in bordered Heegaard Floer homology.
Abstract
We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category. Along the way we prove some foundational results regarding the relevant objects from bordered Heegaard Floer homology,
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics