Upsilon invariants from cyclic branched covers

Antonio Alfieri; Daniele Celoria; Andras Stipsicz

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arXiv · 1809.08269

Upsilon invariants from cyclic branched covers

Antonio Alfieri·Daniele Celoria·Andras Stipsicz

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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 $\Upsilon_m^C (K)$ 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.

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Antonio Alfieri, Daniele Celoria, Andras Stipsicz. 2018-09-21. Upsilon invariants from cyclic branched covers. https://arxiv.org/abs/1809.08269

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