Homology cylinders in knot theory

Details Homology cylinders in knot theory Homology cylinders in knot theory

2008-07-25

arxiv.org/abs/0807.4034v4

Mathematics

Geometric Topology

24 pages, 9 figures

Scientific paper

We compare two concepts treating cobordisms between surfaces: sutured manifolds and homology cylinders. The former ones defined by Gabai are useful to study knots and 3-dimensional manifolds, and the latter are in an important position in the recent theory of the mapping class group, homology cobordisms of surfaces and finite-type invariants. We study a relationship between them by focusing on sutured manifolds associated with a special class of knots which we call homologically fibered knots. Then we use invariants of homology cylinders to give applications to knot theory such as fibering obstructions, Reidemeister torsions and handle numbers of homologically fibered knots.

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