Affiliation:
1. Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA
Abstract
A virtual[Formula: see text]-string is a chord diagram with [Formula: see text] core circles and a collection of arrows between core circles. We consider virtual [Formula: see text]-strings up to virtual homotopy, compositions of flat virtual Reidemeister moves on chord diagrams. Given a virtual 1-string [Formula: see text], Turaev associated a based matrix that encodes invariants of the virtual homotopy class of [Formula: see text]. We generalize Turaev’s method to associate a multistring based matrix to a virtual [Formula: see text]-string, addressing an open problem of Turaev and constructing similar invariants for virtual homotopy classes of virtual [Formula: see text]-strings.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
2 articles.
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1. Parity on based matrices;Journal of Knot Theory and Its Ramifications;2022-02
2. Complexity of virtual multistrings;Communications in Contemporary Mathematics;2021-08-24