Cobordisms of graphs. A sliceness criterion for stably odd knots and related results on cobordisms

TL;DR

This paper extends a sliceness criterion from odd free knots to stably odd free knots and explores related results on knot cobordisms, advancing understanding of knot sliceness conditions.

Contribution

It introduces a sliceness criterion for stably odd free knots, building upon previous work on odd free knots, and provides additional insights into knot cobordism.

Findings

Established a sliceness criterion for stably odd free knots

Provided new results on knot cobordism

Extended previous sliceness criteria to a broader class of knots

Abstract

In [D.A. Fedoseev, V.O. Manturov, A sliceness criterion for odd free knots,arXiv:1707.04923], the authors proved a sliceness criterion for odd free knots: free knots with odd chords. In the present paper we give a similar criterion for stably odd free knots. Some additional results on knot sliceness and cobordism are given.