Turaev genus, knot signature, and the knot homology concordance invariants

TL;DR

This paper establishes bounds on key knot invariants such as signature, tau, and s in relation to the Turaev genus, linking geometric and algebraic knot properties.

Contribution

It introduces new bounds connecting the Turaev genus with knot invariants like signature, tau, and s, enhancing understanding of their interrelations.

Findings

Bounds on knot signature in terms of Turaev genus

Bounds on Ozsvath-Szabo tau invariant in terms of Turaev genus

Bounds on Rasmussen s invariant in terms of Turaev genus

Abstract

We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the Rasmussen s invariant in terms of the Turaev genus of the knot.