Virtual strings and their cobordisms
arXiv:math/0311185
Abstract
A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group. We also discuss connections between virtual strings and virtual knots.
32 pages, 1 figure. This is an extended version of my preprint math.GT/0310218. Section 8.4 on secondary obstructions to sliceness is modified; coverings of strings and higher u-polynomials are added