Cobordism invariants for knots with two indices
Vassily Olegovich Manturov
TL;DR
This paper introduces a new invariant for virtual knots that acts as a sliceness obstruction and detects specific moves, applicable when a certain index condition on chords is met.
Contribution
It develops a novel invariant for virtual knots that is sensitive to the $ riangle$-move and applicable under specific index conditions, advancing knot theory tools.
Findings
Invariant detects sliceness in virtual knots.
Sensitive to $ riangle$-move changes.
Applicable when $ ext{Z}_2 imes ext{Z}_2$-index condition is satisfied.
Abstract
We construct an invariant of virtual knots which is a sliceness obstruction and sensitive to the -move. This invariants works if -index of chords is present.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology