Additivity of Handle Number and Morse-Novikov Number of a-small Knots

Details Additivity of Handle Number and Morse-Novikov Number of a-small Knots Additivity of Handle Number and Morse-Novikov Number of a-small Knots

2011-09-21

arxiv.org/abs/1109.4553v1

Mathematics

Geometric Topology

15 pages, 1 figure

Scientific paper

A knot is an a-small knot if its exterior does not contain closed incompressible surfaces disjoint from some incompressible Seifert surface for the knot. Using circular thin position for knots we prove that the handle number is additive under the connected sum of two a-small knots. As a consequence the Morse-Novikov number turns out to be additive under the connected sum of two a-small knots.

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