Crossing changes in closed 3-braid diagrams

Details Crossing changes in closed 3-braid diagrams Crossing changes in closed 3-braid diagrams

2010-01-10

arxiv.org/abs/1001.1559v1

Mathematics

Geometric Topology

20 pages, 12 figures

Scientific paper

A crossing in a knot is nugatory if changing the crossing does not change the
knot type. Using an invariant of certain types of closed 3-braid diagrams, we
show that if a closed 3-braid contains a nugatory crossing then its braid index
is one or two. This proves a special case of a conjecture on nugatory crossings
due to Xiao-Song Lin.

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