#### Volume 17, issue 1 (2017)

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Notes on the knot concordance invariant Upsilon

### Charles Livingston

Algebraic & Geometric Topology 17 (2017) 111–130
##### Abstract

Ozsváth, Stipsicz and Szabó have defined a knot concordance invariant ${\Upsilon }_{K}$ taking values in the group of piecewise linear functions on the closed interval $\left[0,2\right]$. This paper presents a description of one approach to defining ${\Upsilon }_{K}$ and proving its basic properties.

##### Keywords
knot concordance, Upsilon, four genus, concordance genus, Heegaard Floer
Primary: 57M25
##### Publication
Revised: 24 May 2016
Accepted: 1 June 2016
Published: 26 January 2017
##### Authors
 Charles Livingston Department of Mathematics Indiana University Rawles Hall 831 East Third Street Bloomington, IN 47405-5701 United States