Upsilon invariants from cyclic branched covers

Abstract

We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering $m$-fold cyclic branched covers with $m$ a prime power, this extension provides new knot concordance invariants ${{\rm Y}}_m^C(K)$ of knots in $S^3$. We give computations of these invariants for some families of alternating knots and reprove some independence results in the smooth concordance group.

arXiv comment26 pages, 13 figures. New version fixes typos, minor mistakes and improves readability. Comments are welcome!

References in corpus (13)

• Floer homology and knot complements
• Concordance homomorphisms from knot Floer homology
• Corrigendum to "Knot Floer homology detects fibred knots"
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Cables of thin knots and bordered Heegaard Floer homology
• Floer Simple Manifolds and L-Space Intervals
• Notes on the knot concordance invariant Upsilon
• Seifert forms and concordance
• Computing Knot Floer Homology in Cyclic Branched Covers
• $\tau$-invariants for knots in rational homology spheres
• On concordances in 3-manifolds
• Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers
• An involutive upsilon knot invariant

Cited by in corpus (2)

• On the Upsilon invariant of fibered knots and right-veering open books
• Deformations of lattice cohomology and the upsilon invariant