Notes on the knot concordance invariant Upsilon

By Charles Livingston. 2014

48 citations recorded by the source corpus.

The knot concordance invariant Upsilon, recently defined by Ozsvath, Stipsicz, and Szabo, takes values in the group of piecewise linear functions on the closed interval [0,2]. This paper presents a description of one approach to defining Upsilon and of proving its basic properties related to the knot 3-genus, 4-genus, and concordance genus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dbc9f774d1cbb77e49af8b8e0a30577a889363ff

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In Computational Theory and Mathematics

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. Zolt'an Szab'o
4. M. Hedden
5. Jacob Rasmussen
6. Yi Ni
7. Jennifer Hom
8. Ciprian Manolescu

In Geometry and Topology

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. Zolt'an Szab'o
4. Ciprian Manolescu
5. P. Lisca
6. Jacob Rasmussen
7. John A. Baldwin
8. M. Hedden

In Mathematical Physics

1. A. Stipsicz
2. Peter S. Ozsv'ath
3. Zolt'an Szab'o
4. Ciprian Manolescu
5. Jacob Rasmussen
6. M. Hedden
7. John A. Baldwin
8. Ian Zemke

Citations in the corpus

• Concordance homomorphisms from knot Floer homology (2014, background): “of t-modified knot Floer homology and ΥK(t) The aim of this section is to describe the definition of t-modified knot Floer homology of a knot K ⊂S3 and its corresponding numerical invariant ΥK(t). (See [21] for an alternative description of these constructions.) We describe the definition first for rati”