Finite-Type Invariants of order one for long virtual knots

Abstract

We extend to the long virtual knot case the constructions first presented by A. Henrich and later generalized by the author to the framed virtual knot case. These consist of three Vassiliev invariants of order one, including a universal one, as well as the notions of a based matrix and a singular based matrix and their relation to long flat virtual knots.

arXiv comment20 pages, 24 figures. arXiv admin note: text overlap with arXiv:1509.07530 This paper has been withdrawn as it has been subsumed (together with arXiv:1509.07530) into a paper submitted for publication, whose first draft has been uploaded to arXiv