Introduction to Heegaard Floer homology

E. A. Gorsky<sup>abc

a</sup> Moscow State University
^b International Laboratory of Representation Theory and Mathematical Physics, National Research University Higher School of Economics
^c University of California, Davis, USA

Abstract: Heegaard Floer homology is an invariant of knots, links, and 3-manifolds introduced by Ozsváth and Szabó about 15 years ago. This survey defines Heegaard Floer homology and describes its basic properties. Also discussed is the relation between Heegaard Floer homology and invariants of singularities of curves and surfaces.
Bibliography: 72 titles.

Keywords: knots, links, 3-manifolds, Alexander polynomial, plane curve singularities, Heegaard Floer homology.

UDC: 515.162

MSC: Primary 57M27, 57R58; Secondary 32S25

Received: 29.07.2018

DOI: 10.4213/rm9849

 English version: Russian Mathematical Surveys, 2019, 74:1, 1–35

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