Work

Lattice homology, formality, and plumbed L-space links

Year: 2024

Type: article

Abstract: We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth, Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in rational homology 3-spheres, the link lattice complex is homotopy equivalent to the link Floer complex as an A_{\infty} -module. Additionally, we prove that the link Floer complex of a plumbed L-space link is a free resolution of its homology. As a consequence, we give an algorithm to compute the link Floer complexes of plumbed L-space links, in particular of algebraic links, from their multivariable Alexander polynomial.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1562

Authors: Maciej Borodzik, Beibei Liu, Ian Zemke

Institutions: Polish Academy of Sciences, The Ohio State University, University of Oregon

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: New Perspectives in Heegaard Floer Homology, Link Floer Homology and Kleinian Groups, PostDoctoral Research Fellowship