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．

　　（Doctor 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： 25 July 2018.