Department of Mathematics, Tokyo Institute of Technology,
2-12-1 Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan.

E-mail address: sakasai + @math.titech.ac.jp
(Please remove +)

Topology, mapping class groups of surfaces, 3-dimensional manifolds, homology cobordisms, noncommutative algebra etc...

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.

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.

1. (With Hiroshi Goda) Homology cylinders in knot theory.
   arXiv:math.GT/0807.4034, (28 July 2008).

2. (With Hiroshi Goda) Abelian quotients of monoids of homology cylinders.
   arXiv:math.GT/0905.4775, (29 May 2009).

3. Lagrangian mapping class groups from group homological point of view.
   arXiv:math.GT/0910.5262, (27 Oct 2009).

1. Genus invariants of closed 3-manifolds associated to homology cobordisms of surfaces.
   Download (7 October 2007)

2. Computations of noncommutative Alexander invariants for string links.
   Download (30 November 2007)

3. Factorization formulas of higher-order Alexander invariants for homological fibered knots.
   Download (1 September 2009)

• Mapping class groups, groups of homology cobordisms of surfaces and invariants of 3-manifolds.
  Doctoral Dissertation, The University of Tokyo, 2006.
  Almost all of the contents were published in the papers 1,2,3,5.

• "T4M6" is the Mathematica version of the software "Teruaki", a mapping class group calculator, originally produced by Professor Ahara.
  (You can download the original "Teruaki" from his homepage.)
• This version (for Mathematica 6) is a joint work with Masaaki Suzuki.
• T4M6 download: [manual (please read first)], [closed surface version], [surface with boundary version].

• Another Homepage written in Japanese
• arXiv:math
• LiE
• Groups of Diffeomorphisms 2006 (GD2006)
• CTQM: The center for the topology and quantization of moduli spaces
• MPIM: Max Plank Institute for Mathematics