Exact triangle for fibered Dehn twists

TL;DR

This paper generalizes Seidel's exact sequence in symplectic Floer theory to fibered Dehn twists using quilted Floer theory and applies it to construct Floer and Khovanov-Rozansky exact triangles in the context of moduli spaces of bundles.

Contribution

It introduces a generalized exact sequence for fibered Dehn twists and applies it to new constructions in Lagrangian Floer theory related to moduli spaces.

Findings

Generalized Seidel's exact sequence to fibered Dehn twists

Constructed Floer and Khovanov-Rozansky exact triangles

Extended Floer theory applications to moduli spaces

Abstract

We use quilted Floer theory to generalize Seidel's long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply it to construct versions of the Floer and Khovanov-Rozansky exact triangles in Lagrangian Floer theory of moduli spaces of bundles.