Mathematics – Geometric Topology
Scientific paper
2008-07-25
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.
Goda Hiroshi
Sakasai Takuya
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