# Upsilon invariants of L-space cable knots

## TL;DR

This paper provides a formula to compute the Upsilon invariant for L-space cable knots, linking it to known invariants of the base knot and torus knots, and explores its properties as a concordance invariant.

## Contribution

It introduces a new explicit formula for the Upsilon invariant of L-space cable knots, expanding the computational tools for knot concordance invariants.

## Key findings

- Derived a formula relating Upsilon of cable knots to base and torus knots
- Computed integral Upsilon values for iterated cable knots
- Demonstrated the Upsilon invariant as a rational-valued concordance invariant

## Abstract

We give a formula of the Upsilon invariant of any L-space cable knot $K_{p,q}$ using $p,\Upsilon_K$ and $\Upsilon_{T_{p,q}}$. The integral value of the Upsilon invariant gives a ${\mathbb Q}$-valued knot concordance invariant. We compute the integral values for L-space iterated cable knots.