2012/12/28 by Jonathan M. Bloom, Bloom, Jonathan M.
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.CO #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.1212.6467
43 pages, 19 figures
arxiv created 2012/12/28 · openalex publication_date 2012/12/28 · arxiv updated 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.