Homepage of Takuya SAKASAI

Associate Professor

Graduate School of Mathematical Sciences, The University of Tokyo,
3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan.

E-mail address: sakasai + @ms.u-tokyo.ac.jp
(Please remove +)

Research Interests
  1. The Johnson homomorphism and the third rational cohomology group of the Torelli group.
    Topology and its Applications 148 (2005), 83-111.

  2. Homology cylinders and the acyclic closure of a free group.
    Algebraic & Geometric Topology 6 (2006), 603-631.

  3. The second Johnson homomorphism and the second rational cohomology of the Johnson kernel.
    Mathematical Proceedings of the Cambridge Philosophical Society 143 (2007), 627-648.

  4. The symplecticity of the Magnus representation for homology cobordisms of surfaces.
    Bulletin of the Australian Mathematical Society 76 (2007), 421-431.

  5. The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces.
    Algebraic & Geometric Topology 8 (2008), 803-848.

  6. (With Hiroshi Goda) Abelian quotients of monoids of homology cylinders.
    Geometriae Dedicata 151 (2011), 387-396.

  7. (With Hiroshi Goda) Factorization formulas and computations of higher-order Alexander invariants for homologically fibered knots.
    Journal of Knot Theory and Its Ramifications 20 (2011), 1355-1380.

  8. Lagrangian mapping class groups from a group homological point of view.
    Algebraic & Geometric Topology 12 (2012), 267-291.

  9. (With Hiroshi Goda) Homology cylinders and sutured manifolds for homologically fibered knots.
    [The title was changed from Homology cylinders in knot theory in the preprint version.]
    Tokyo Journal of Mathematics 36, Number 1 (2013), 85-111.

  10. (With Shigeyuki Morita and Masaaki Suzuki) Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra.
    Duke Mathematical Journal 162, Number 5 (2013), 965-1002.

  11. (With Shigeyuki Morita and Masaaki Suzuki) Integral Euler characteristic of Out F_{11}.
    Experimental Mathematics 24, (2015), 93-97.

  12. (With Shigeyuki Morita and Masaaki Suzuki) Computations in formal symplectic geometry and characteristic classes of moduli spaces.
    Quantum Topology 6 (2015), 139-182.

  13. The Magnus representation and homology cobordism groups of homology cylinders.
    Journal of Mathematical Sciences, the University of Tokyo 22 (2015), 741-770.

  14. (With Shigeyuki Morita and Masaaki Suzuki) Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras.
    Advances in Mathematics 282 (2015), 291-334.

  15. (With Shigeyuki Morita and Masaaki Suzuki) Symmetry of symplectic derivation Lie algebras of free Lie algebras.
    RIMS Kôkyûroku Bessatsu B66 (2017), 185-193.

  16. (With Shigeyuki Morita and Masaaki Suzuki) An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra.
    Experimental Mathematics 27, (2018), 302-315.

  17. (With Shigeyuki Morita and Masaaki Suzuki) Torelli group, Johnson kernel and invariants of homology spheres.
    Quantum Topology 11 (2020), 379-410.

  18. (With Gwénaël Massuyeau) Morita's trace maps on the group of homology cobordisms.
    Journal of Topology and Analysis, 12 (2020), 775-818.

Proceedings and Surveys
  1. Higher-order Alexander invariants for homology cobordisms of a surface.
    Intelligence of Low Dimensional Topology 2006, Series on Knots and Everything 40, 271-278.

  2. Johnson's homomorphisms and the rational cohomology of subgroups of the mapping class group.
    Groups of Diffeomorphisms, Advanced studies in pure mathematics 52, (2008), 93-109.

  3. A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces.
    Handbook of Teichmüller theory volume III (editor: A. Papadopoulos), (2012), 531-594.

  4. Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces.
    Winter Braids Lecture Notes 3, (2016), Course no IV 1-25.

  1. (With Shigeyuki Morita and Masaaki Suzuki) Secondary characteristic classes for subgroups of automorphism groups of free groups.
    arXiv:math.AT/1512.06365, (22 Dec 2015).

T4M7 (Teruaki for Mathematica 7)