| kitayama@ms.u-tokyo.ac.jp | |
| TEL | +81-3-5465-8329 | 48329（ext.） |
| Room | 368, Graduate School of Mathematical Sciences Bldg. 3F, Komaba Campus |
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Research Field
Topology
Research Subject
Low dimensional topology and geometry of character varieties
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.
Keywords
3-manifolds, discrete groups, character varieties, torsion invariants, Morse-Novikov theory