Associate Professor
Research interests
3-manifolds, discrete groups, character varieties, torsion invariants, Morse-Novikov theory
Current research

I am working on 3-manifold topology from aspects of covering spaces, especially, with non-commutative deck transformations. My research is based, in particular, on topological invariants associated to geometric structures or representations of fundamental groups, moduli spaces of linear representations of finitely generated groups, and a certain generalization of the Morse theory for closed 1-forms. I am trying to establish foundations of applying the geometry of moduli spaces of higher-dimensional linear representations to low-dimensional topology. As recent interactive developments between 3-manifold topology and geometric group theory have been remarkable, it is also an important project to extend ideas in the study of 3-manifold groups to that of general discrete groups.

Selected publications
  1. Twisted Alexander polynomials and incompressible surfaces given by ideal points, Journal of Mathematical Sciences, the University of Tokyo 22 (2015), 877-891.
  2. The virtual fibering theorem for 3-manifolds (with Stefan Friedl), L'Enseignement Mathématique 60 (2014), 79-107.
  3. Poincaré duality and degrees of twisted Alexander polynomials (with Stefan Friedl and Taehee Kim), Indiana University Mathematics Journal 61 (2012), 147-192.
  4. Homology cylinders of higher-order, Algebraic and Geometric Topology 12 (2012), 1585-1605.
  5. Non-commutative Reidemeister torsion and Morse-Novikov theory, Proceedings of the American Mathematical Society 138 (2010), 3345-3360.

Memberships, activities and


The Mathematical Society of Japan