Total curvatures of holonomic links

Details Total curvatures of holonomic links Total curvatures of holonomic links

1999-05-07

arxiv.org/abs/math/9905040v2

Mathematics

Geometric Topology

13 pages, 5 figures. 5 lines in the proof of Theorem 1 has been changed

Scientific paper

A differential geometric characterization of the braid-index of a link is found. After multiplication by 2pi, it equals the infimum of the sum of total curvature and total absolute torsion over holonomic representatives of the link. Upper and lower bounds for the infimum of total curvature over holonomic representatives of a link are given in terms of its braid- and bridge-index. Examples showing that these bounds are sharp are constructed.

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