分野別セミナー

This is a joint work with Takuya Sakasai.
Two concepts, sutured manifolds and homology cylinders,
treating cobordisms between surfaces are compared.
The former ones defined by Gabai are useful to study knots
and 3-dimensional manifolds, and the latter are
in an important position in the recent theory of the mapping class group,
homology cobordisms of surfaces and finite-type invariants.
We study a relationship between them by considering
which knot has a homology cylinder as a complementary sutured manifold
that is a sutured manifold obtained from a knot complement.
As the answer to it, `homological fibered knots' are introduced.
They are characterized by their Alexander polynomials and genera.
Then we use some invariants of homology cylinders to give applications
such as fibering obstructions and handle numbers of homological fibered
knots.