"Parallelism of two strings in alternating tangles (revised version)"
- abstract
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We consider the parallelism of two strings in alternating tangles.
We show that if there is a pair of parallel strings
in an alternating tangle
then its alternating diagrams satify certain conditions.
As a corollary, for knots admitting a decomposition
into two alternating tangles with two or three strings,
we prove that its non-trivial Dehn surgery yields a 3-manifold
with essential lamination.
Hence they have property P and satisfy the cabling conjecture.
