Algebraic & Geometric Topology

The concordance invariant tau in link grid homology

Alberto Cavallo

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We introduce a generalization of the Ozsváth–Szabó τ –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.

Article information

Algebr. Geom. Topol., Volume 18, Number 4 (2018), 1917-1951.

Received: 12 January 2016
Revised: 6 September 2017
Accepted: 6 February 2018
First available in Project Euclid: 3 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

link invariants Heegaard Floer homology Concordance


Cavallo, Alberto. The concordance invariant tau in link grid homology. Algebr. Geom. Topol. 18 (2018), no. 4, 1917--1951. doi:10.2140/agt.2018.18.1917.

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