Heegaard Floer homology and integer surgeries on links

By Ciprian Manolescu, Peter S. Ozsv'ath. Geometry & Topology, 2010

84 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/dd040e30eb04a85f149683e613d31f7077a78283

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

In Neurology

Citations in the corpus

A survey of Heegaard Floer homology (2013, background): “sverse knots in contact 3-manifolds, cf. Ozsv´ath, Szabo´, and Thurston [81]. The hat version of HF is considerably simpler to compute than the other ﬂavors. It took Manolescu, Ozsv´ath, and Thurston [56, 58] several years to bring the grid diagram approach to fruition and show that all ﬂavors of HF”
Moving basepoints and the induced automorphisms of link Floer homology (2011, background): “n the stabilization map FeG,G′, deﬁned in terms of the snail domains, is the same as the naturality map FG,G′ in MorD(A l)(CFG,CFG′). Proof. By naturality, we know that FG,G′FG′,G = Id in K(Al). From [MO] we know that FG′,G = FeG′,G in K(Al). Finally, it is easy to check that the chain map FeG′,GFeG”
Connected sums and involutive knot Floer homology (2017, background): “ the construction of the maps in [Zem19] are maps for adding or removing basepoints on a link component. These are the quasi-stabilization maps. The quasistabilization operation was rst considered in [MO10]. The author considered them further in [Zem17], proving several useful results. According to ”
Link cobordisms and functoriality in link Floer homology (2016, methodology): “tive diagrams for (S1 S2)#k and quasi-stabilization of Heegaard triples. In this subsection we review the results from [Zem16] about quasi-stabilization and triangle maps. We rst review a result from [MO10], which will be useful in showing that quasi-stabilization commutes with the change of diagram”
Quasi-stabilization and basepoint moving maps in link Floer homology (2016, methodology): “izing Heegaard triples along a single curve. We now consider Heegaard triples which are quasi-stabilized along a single s curve which is allowed to run through the diagram. This was rst considered in [MO10]. We state [MO10, Prop. 5.2], which considers the quasi-stabilized conguration shown in Figure”