Parity and Cobordisms of Free Knots

Details Parity and Cobordisms of Free Knots Parity and Cobordisms of Free Knots

2010-01-16

arxiv.org/abs/1001.2827v3

Mathematics

Geometric Topology

A result on cobordisms of higher genus with some constraints is added; A list of problems is added

Scientific paper

In the present paper, we construct a simple invariant which provides a sliceness obstruction for {\em free knots}. This obstruction provides a new point of view to the problem of studying cobordisms of curves immersed in 2-surfaces, a problem previously studied by Carter, Turaev, Orr, and others. The obstruction to sliceness is constructed by using the notion of {\em parity} recently introduced by the author into the study of virtual knots and their modifications. This invariant turns out to be an obstruction for cobordisms of higher genera with some additional constraints.

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