Notes on the knot concordance invariant Upsilon

Livingston, Charles

doi:10.2140/agt.2017.17.111

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Notes on the knot concordance invariant Upsilon

Charles Livingston

Algebraic & Geometric Topology 17 (2017) 111–130

DOI: 10.2140/agt.2017.17.111

Abstract

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

Keywords

knot concordance, Upsilon, four genus, concordance genus, Heegaard Floer

Mathematical Subject Classification 2010

Primary: 57M25

References

Publication

Received: 4 April 2015

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

Volume 17, issue 1 (2017)