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Homology cylinders and sutured manifolds for homologically fibered knots

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.

preprint2013arXivOpen access
Hiroshi GodaTakuya Sakasai
math.ATmath.GT
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Hiroshi GodaTakuya Sakasai

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