Floer field theory for coprime rank and degree

Katrin Wehrheim, Chris Woodward

Research output: Contribution to journalArticlepeer-review

Abstract

We construct partial category-valued field theories in (2 + 1)-dimensions using Lagrangian Floer theory in moduli spaces of central-curvature unitary connections with fixed determinant of rank r and degree d where r, d are coprime positive integers. These theories assign the Fukaya category of the moduli space to a closed, connected, oriented surface, and a functor between extended Fukaya categories with a connected bordism between two surfaces. We obtain the latter by combining Cerf theory with holomorphic quilt invariants. These functors satisfy the natural composition law.

Original languageEnglish (US)
Pages (from-to)2035-2088
Number of pages54
JournalIndiana University Mathematics Journal
Volume69
Issue number6
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics

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