## Algebraic & Geometric Topology

### The concordance invariant tau in link grid homology

Alberto Cavallo

#### Abstract

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

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

Dates
Revised: 6 September 2017
Accepted: 6 February 2018
First available in Project Euclid: 3 May 2018

https://projecteuclid.org/euclid.agt/1525312823

Digital Object Identifier
doi:10.2140/agt.2018.18.1917

Mathematical Reviews number (MathSciNet)
MR3797061

Zentralblatt MATH identifier
06867652

#### Citation

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. https://projecteuclid.org/euclid.agt/1525312823

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