Volume 18, issue 4 (2018)

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The concordance invariant tau in link grid homology

Alberto Cavallo

Algebraic & Geometric Topology 18 (2018) 1917–1951
Abstract

We introduce a generalization of the Ozsváth–Szabó $\tau$–invariant to links by studying a filtered version of link grid homology. We prove that this invariant remains unchanged under strong concordance and we show that it produces a lower bound for the slice genus of a link. We show that this bound is sharp for torus links and we also give an application to Legendrian link invariants in the standard contact $3$–sphere.

Keywords
link invariants, Heegaard Floer homology, Concordance
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Publication
Revised: 6 September 2017
Accepted: 6 February 2018
Published: 26 April 2018
Authors
 Alberto Cavallo Department of Mathematics and its Applications Alfred Renyi Institute of Mathematics Budapest Hungary