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.
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