2025/05/02 by Guillem Cazassus, Cazassus, Guillem
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2505.01362
openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the Morse complex of a compact Lie monoid can be given the structure of an f-bialgebra, a chain-level version of bialgebras introduced in [CHM24]; and that this assignment defines an ∞-functor. As a consequence, we obtain two other ∞-functors mapping closed smooth manifolds to their Morse complexes with their A_∞-coalgebra structures; and closed smooth manifolds with compact Lie group actions to their Morse complexes, with a ``u-bimodule'' structure (a bimodule version for f-bialgebras).