Heegaard Floer homology and integer surgeries on links
arXiv:1011.1317 · doi:10.2140/gt.2025.29.2783
Abstract
Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a complete systems of hyperboxes consists of chain complexes for (some versions of) the link Floer homology of L and all its sublinks, together with several chain maps between these complexes. Further, we introduce a way of presenting closed four-manifolds with b_2^+ > 1 by four-colored framed links in the three-sphere. Given a link presentation of this kind for a four-manifold X, we then describe the Ozsvath-Szabo mixed invariants of X in terms of a complete system of hyperboxes for the link. Finally, we explain how a grid diagram produces a particular complete system of hyperboxes for the corresponding link.
234 pages, 56 figures; final version, to appear in Geometry & Topology
References in corpus (3)
Cited by in corpus (21)
- Link cobordisms and functoriality in link Floer homology
- Moving basepoints and the induced automorphisms of link Floer homology
- On the equivalence of Legendrian and transverse invariants in knot Floer homology
- Connected sums and involutive knot Floer homology
- -space surgeries on links
- Graph cobordisms and Heegaard Floer homology
- A tour of bordered Floer theory
- Sutured Floer homology and invariants of Legendrian and transverse knots
- Immersed concordances of links and Heegaard Floer homology
- Heegaard Floer homology of surgeries on two-bridge links
- Heegaard Floer homology of L-space links with two components
- Knot lattice homology in L-spaces
- Strong Khovanov-Floer Theories and Functoriality
- Heegaard Floer Homology and Triple Cup Products
- Knots in lattice homology
- Links of Second Smallest Knot Floer Homology
- L-space surgeries on 2-component L-space links
- Unoriented Cobordism Maps on Link Floer Homology
- Framed Floer Homology
- Contact (+1)-surgeries along Legendrian Two-component Links
- Four manifolds with no smooth spines