Cobordisms of Free Knots and Gauss Words
Denis Petrovich Ilyutko, Vassily Olegovich Manturov
TL;DR
This paper introduces a new invariant for free knots, enabling the detection of non-trivial cobordism classes among free knots and links, which are represented by homotopy classes of Gauss words.
Contribution
A novel strong invariant for free knots is defined, advancing the understanding of cobordism relations in the context of Gauss words and free knots.
Findings
The invariant can distinguish non-cobordant free knots.
It detects free knots not cobordant to the trivial knot.
The work advances the classification of free knots via cobordism.
Abstract
We investigate cobordisms of free knots. Free knots and links are also called homotopy classes of Gauss words and phrases. We define a new strong invariant of free knots which allows to detect free knots not cobordant to the trivial one.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics