M. Ishikawa (Keio)

Title: Positive flow-spines and contact 3-manifolds

Abstract: "A contact structure is a smooth distribution of hyperplanes
on an odd-dimensional manifold that is non-integrable everywhere. In
the case of dimension 3, there is a nice relationship between open
book decompositions of 3-manifolds and contact structures up to
contactomorphisms, called Giroux correspondence. A flow-spine is a
spine of a 3-manifold admitting a flow such that it is transverse to
the spine and the flow in the complement of the spine is diffeomorphic
to a constant flow in an open ball. In this talk, we introduce some
results in progress that give a correspondence between contact
structures and positive flow-spines by regarding Reeb vector fields as
flows of spines. This is a joint work with Ippei Ishii, Yuya Koda and
Hironobu Naoe."