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.

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