Strict Equivalence of Multi-Virtual Linkoids

Abstract: We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual knots and links, we obtain new invariants for strict virtual linkoids. Generalized bracket polynomial invariants and generalized loop bracket polynomial invariants (for planar strict virtual linkoids) are studied in this context. The talk defines virtual polar links where there are degree two nodes in virtual link diagrams across which isotopies are forbidden. The talk will show how multi-virtual theory and its concepts can be applied to obtain invariants for polar virtual links. The talk will also discuss graph theoretic background to the talk and many open problems and ideas that are associated with this subject.

mathematical physicsalgebraic topologycombinatoricsgeometric topologyrings and algebrasrepresentation theory

Audience: researchers in the topic

Knots, graphs and groups

Series comments: Zoom - Meeting ID: 818 6674 5751 Passcode: 141592

Link: us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09

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