D. Freund

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math.GT2017

Complexity of virtual multistrings

David Freund

A virtual $n$ -string $α$ is a collection of $n$ oriented smooth generic loops on a surface $M$ . A stabilization of $α$ is a surgery that results in attaching a handle to $M$ along…

math.GT2017

Multistring based matrices

David Freund

A virtual $n$ -string is a chord diagram with $n$ core circles and a collection of arrows between core circles. We consider virtual $n$ -strings up to virtual homotopy, compositions…

math.GT2017

Minimizing intersection points of curves under virtual homotopy

Vladimir Chernov, David Freund, Rustam Sadykov

A flat virtual link is a finite collection of oriented closed curves $L$ on an oriented surface $M$ considered up to virtual homotopy, i.e., a composition of elementary s…