PRIME DECOMPOSITIONS OF VIRTUAL KNOTS
Abstract
We prove that any virtual knot can be presented as a connected sum of several prime and trivial virtual knots. Prime summands of the presentation are defined uniquely, i.e. they are determined by the original knot. We introduce two types of reductions on the set of knots in thickened surfaces and prove that the result of any sequence of reductions exists and is defined uniquely.
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Review
For citations:
Korablev P.G. PRIME DECOMPOSITIONS OF VIRTUAL KNOTS. The Bulletin of Kemerovo State University. 2011;(3-1):63-67. (In Russ.)
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