2006/11/16 by Thomas E. Mark, Mark, Thomas E.
Mathematics · #57M #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0611511
openalex publication_date 2006/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by conjectures in Heegaard Floer homology, we introduce an invariant HC(Y) of the cohomology ring of a closed 3-manifold Y whose behavior mimics that of the Heegaard Floer homology HF^∞(Y,s) for s a torsion spin-c structure. We derive from this a numerical invariant h(Y), and obtain upper and lower bounds on h(Y). We describe the behavior of h(Y) under connected sum, and deduce some topological consequences. Examples show that the structure of HC(Y) can be surprisingly complicated, even for 3-manifolds with comparatively simple cohomology rings.