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Homology cylinders and sutured manifolds for homologically fibered knots

Research paper by Hiroshi Goda, Takuya Sakasai

Indexed on: 25 Mar '13Published on: 25 Mar '13Published in: Mathematics - Geometric Topology



Abstract

Sutured manifolds defined by Gabai are useful in the geometrical study of knots and 3-dimensional manifolds. On the other hand, homology cylinders are in an important position in the recent theory of 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 {\it 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.