The combinatorics of Morse theory with boundary

Abstract

We prove several combinatorial results on path algebras over discrete structures related to directed graphs. These results are motivated by Morse theory on a manifold with boundary and, more generally, by Floer theory on a configuration space with boundary. Their purpose is to organize cobordism relationships among moduli spaces in order to define new algebraic invariants. We discuss applications to the Morse and Fukaya categories, and to work with John Baldwin on a bordered monopole Floer theory.

43 pages, 19 figures

References in corpus (5)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Fukaya categories of the torus and Dehn surgery
• Arithmetic mirror symmetry for the 2-torus
• A tour of bordered Floer theory
• Floer's chain complexes for Lagrangian submanifolds in symplectic manifolds with concave ends

Cited by in corpus (6)

• A contact invariant in sutured monopole homology
• Loss Landscapes of Regularized Linear Autoencoders
• A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture
• The space of sections of a smooth function
• Exotic symplectomorphisms and contact circle actions
• Embedded Morse theory and relative splitting of cobordisms of manifolds