Research interests

  Keywords

Algebraic topology  Combinatorial group theory  Group cohomology 
Representation theory (Highest weight theory)

Automorphism groups of free groups  Mapping class groups of surfaces 
Braid groups  General linear groups

Twisted cohomology  Unstable cohomology

  



 

Tools for our research

 Presentations of groups Commutator Calculus
 Lie algebras associated to central ser. of groups

 Five-term exact seq. LHS spectral seq.
 Free Lie algebras Hall basis Lie algebras of derivations

 Johnson homomorphisms Magnus representations

Achieved by the integration of beyond generations works by
  Andreadakis, Johnson, Morita, Pettet, S., Enomoto,
  Massuyeau, Sakasai, Bartholdi and Darné. 



   Short Summary

    here (Oct. 2016 version.)


   Research Biography

 Sep. 2017〜 Mar. 2018, The University of Bonn / Tokyo University of Science

    The Andreadakis conjecture for degree 3 case.

 Apr. 2011〜Aug. 2017, Tokyo University of Science

    The Andreadakis conjecture and cohomology groups for IA_3.

    The structure of the SL_m-universal representation rings of free groups,
      The Johnson-Morita theory for the ring of Fricke characters of free groups and free abelian groups,

    The Johnson cokernel of Basis-conjugating automorphisms of free groups and free metabelian groups,
      The Andreadakis conjecture for the lower triangular automorphism groups of free groups,
      Presentations for the lower triangular automorphism groups of free groups.

   (Joint work with Prof. Dr. Hatakenaka) A descending filtration of the ring of Fricke characters of free groups,
      The structure of the ring of Fricke characters of free abelian groups.

 Oct. 2008〜Mar. 2011, Kyoto University

   A generalization of the Chen integrals on free groups,
      The infinite generation of the kernel of the Magnus representation,
      The stable cokernel of the Johnson homomorphisms associated to the lower central series of IA_n,
      The augmentation quotients of IA_n.

   (Joint work with Prof. Dr. Enomoto) The GL-decomposition of the Johnson cokernels,
      Twisted cohomology groups of the automorphism groups of free nilpotent groups,
      New obstructions for the surjectivity of the Johnson homomorphisms of the mapping class groups.

   (Joint work with Prof. Dr. Fujii) Geodesic elements and growth functions of braid groups.

 Apr. 2007〜Sep. 2008, Osaka University

   The images of the Andreadakis-Johnson filtration of Aut F_n,
    The Andreadakis-Johnson filtration of the McCool stabilizer subgroups.

 Apr. 2002〜Mar.2007, The University of Tokyo

  (JSPS Research Fellow(PD))The Johnson cokernel of the automorphism groups of free metabelian groups.

  (Docter course)A generalization of Morita's trace maps, Twisted second cohomology groups of Aut F_n.

  (Master course)Twisted first cohomology groups of Aut F_n,
            Twisted cohomology groups of B_3,
            Cohomology groups of the congruence-IA automorphism groups.




 Last update: 1 April 2018.