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.

24 pages, 9 figures, The title has been changed

References in corpus (1)

• Knots, sutures and excision

Cited by in corpus (7)

• The decategorification of sutured Floer homology
• Hidden torsion, 3-manifolds, and homology cobordism
• Homology cylinders of higher-order
• Factorization formulas and computations of higher-order Alexander invariants for homologically fibered knots
• The Magnus representation and homology cobordism groups of homology cylinders
• A non-commutative Reidemeister-Turaev torsion of homology cylinders
• Non-commutative Reidemeister torsion and Morse-Novikov theory