Notes on the knot concordance invariant Upsilon

Abstract

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.

This version includes revisions that were made before the final acceptance by AGT

References in corpus (1)

• Floer homology and knot complements

Cited by in corpus (21)

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• The ${\nu }^{+}$-equivalence classes of genus one knots
• The upsilon invariant at 1 of 3-braid knots
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• On sums of torus knots concordant to alternating knots
• Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
• An involutive upsilon knot invariant
• A note on the four-dimensional clasp number of knots
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• The four-genus of connected sums of torus knots
• Upsilon invariants from cyclic branched covers
• On the secondary Upsilon invariant
• Hyperbolic L-space knots not concordant to algebraic knots
• Deformations of lattice cohomology and the upsilon invariant
• On the Upsilon invariant of fibered knots and right-veering open books
• Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex
• A family of concordance homomorphisms from Khovanov homology