## Tokyo Journal of Mathematics

### Homology Cylinders and Sutured Manifolds for Homologically Fibered Knots

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 85-111.

Dates
First available in Project Euclid: 22 July 2013

https://projecteuclid.org/euclid.tjm/1374497513

Digital Object Identifier
doi:10.3836/tjm/1374497513

Mathematical Reviews number (MathSciNet)
MR3112377

Zentralblatt MATH identifier
1287.57022

#### Citation

GODA, Hiroshi; SAKASAI, Takuya. Homology Cylinders and Sutured Manifolds for Homologically Fibered Knots. Tokyo J. Math. 36 (2013), no. 1, 85--111. doi:10.3836/tjm/1374497513. https://projecteuclid.org/euclid.tjm/1374497513

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