Finite-Type Invariants of Order One for Framed Virtual Knots

Abstract

A. Henrich proved the existence of the universal finite-type invariant of order one for virtual knots. We extend the construction and the methods of her paper to framed virtual knots. To do so, we introduce the notions of virtual strings and based matrices for framed flat virtual knots.

arXiv comment18 pages, 16 figures This paper has been withdrawn as it has been subsumed (together with arXiv:1602.08138) into a paper submitted for publication, whose first draft has been uploaded to arXiv