Triple products and cohomological invariants for closed three-manifolds
Geometric Topology
2009-09-29 v3
Abstract
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^\infty(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.
Keywords
Cite
@article{arxiv.math/0611511,
title = {Triple products and cohomological invariants for closed three-manifolds},
author = {Thomas E. Mark},
journal= {arXiv preprint arXiv:math/0611511},
year = {2009}
}
Comments
Edited to reflect referee's suggestions; expanded section 4 including exposition of universal coefficients spectral sequence. This version to appear in Michigan Math. J