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) An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra.
    To appear in Experimental Mathematics, arXiv:math.AT/1608.07645, (30 Aug 2016).

  16. (With Shigeyuki Morita and Masaaki Suzuki) Symmetry of symplectic derivation Lie algebras of free Lie algebras.
    To appear in RIMS Kôkyûroku Bessatsu, arXiv:math.AT/1109.3963, (20 Sep 2011).

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.
    submitted, 31 pages (2017).

  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).

  2. (With Gwénaël Massuyeau) Morita's trace maps on the group of homology cobordisms.
    arXiv:math.GT/1606.08244, (28 Jun 2016).

T4M7 (Teruaki for Mathematica 7)