Virtual Crossing Realization

Details Virtual Crossing Realization Virtual Crossing Realization

2003-03-06

arxiv.org/abs/math/0303077v6

J. Knot Theory Ramifications 14 (2005) 931-951.

Mathematics

Geometric Topology

21 pages, 10 figures. To appear in J. Knot Theory Ramifications. Version 6 includes revisions suggested by the reviewer

Scientific paper

We study virtual isotopy sequences with classical initial and final diagrams, asking when such a sequence can be changed into a classical isotopy sequence by replacing virtual crossings with classical crossings. An example of a sequence for which no such virtual crossing realization exists is given. A conjecture on conditions for realizability of virtual isotopy sequences is proposed, and a sufficient condition for realizability is found. The conjecture is reformulated in terms of 2-knots and knots in thickened surfaces.

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