|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Heegaard Floer homology
and integer surgeries on links
Ciprian Manolescu and Peter Ozsváth |
|
Geometry & Topology 29 (2025) 2783–3062
|
 |
Abstract |
|
Let be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on in terms of some data associated to , which we call a complete system of hyperboxes for . Roughly, a complete system of hyperboxes consists of chain complexes for (some versions of) the link Floer homology of and all its sublinks, together with several chain maps between these complexes. Further, we introduce a way of presenting closed four-manifolds with by four-colored framed links in the three-sphere. Given a link presentation of this kind for a four-manifold , we then describe the Ozsváth–Szabó mixed invariants of 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. |
Keywords
three-manifolds, link Floer homology, mixed invariants,
surgery formula
|
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57R57
|
References |
Publication
Received: 6 April 2017
Revised: 18 November 2022
Accepted: 13 July 2024
Published: 22 September 2025
Proposed: Tomasz S Mrowka
Seconded: András I Stipsicz, Cameron Gordon
|
Authors |
| Ciprian Manolescu | |
| Department of Mathematics Stanford University Stanford, CA United States |
|
| Peter Ozsváth | |
| Department of Mathematics Princeton University Princeton, NJ United States |
|
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
