ON PRIME DECOMPOSITIONS OF KNOTS IN THICKENED SURFACES
Abstract
It is well known that any knot in S3 can be represented as a connected sum of prime summands. Moreover, the summands are determined uniquely. This is the famous theorem of H. Schubert (1949). Is a similar result true for knots in thickened surfaces, that is, in 3-manifolds of the type F х I, where F is a closed orientable surface? It turns out that the existence theorem is true but the uniqueness theorem is false (there are counterexamples). In the paper we describe the general structure ofall possible counterexamples.
References
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Review
For citations:
Matveev S.V. ON PRIME DECOMPOSITIONS OF KNOTS IN THICKENED SURFACES. The Bulletin of Kemerovo State University. 2011;(3-1):67-72. (In Russ.)
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