Homology cylinders in knot theory

In a recent study of mapping class groups of surfaces and finite-type invariants of 3-manifolds, homology cylinders
play an important role. We observe a relationship between
homology cylinders and sutured manifolds associated with a special class of knots which we call homologically fibered knots.
Then we discuss the (non-)fiberedness problem of
homologically fibered knots by using Johnson homomorphisms
and clasper surgery theory.
This is a joint work with Hiroshi Goda (Tokyo University of
Agriculture and Technology).