A faithful linear-categorical action of the mapping class group of a surface with boundary

TL;DR

This paper demonstrates that the mapping class group acts faithfully on bordered Floer homology in a specific spin^c-structure, providing an accessible introduction to the subject.

Contribution

It establishes the faithfulness of the mapping class group action on bordered Floer homology in a particular spin^c-structure, with an emphasis on accessibility.

Findings

Mapping class group acts faithfully on bordered Floer homology

The work is partly introductory and accessible without Floer homology background

Provides new insights into the relationship between surface diffeomorphisms and Floer homology

Abstract

We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin^c-structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.