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, characteristic classes of bundles,
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.

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.
   To appear in Algebraic & Geometric Topology.
   arXiv:math.GT/0910.5262, (1 Dec 2011, revised version).

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 Oct 2010, revised version).

2. A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces.
   arXiv:math.GT/1005.5501, (17 Jan 2011, revised version).
   Submitted to "Handbook of Teichmueller theory, volume III" (editor: A. Papadopoulos)

3. (With Shigeyuki Morita and Masaaki Suzuki) Abelianizations of derivation Lie algebras of free associative algebra and free Lie algebra.
   arXiv:math.AT/1107.3686, (20 Jul 2011).

4. The Magnus representation and homology cobordism groups of homology cylinders.
   arXiv:math.GT/1108.6111, (1 Sep 2011).

5. (With Shigeyuki Morita and Masaaki Suzuki) Symmetry of symplectic derivation Lie algebras of free Lie algebras.
   arXiv:math.AT/1109.3963, (20 Sep 2011).

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)

• 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)
• QGM: Centre for Quantum Geometry of Moduli spaces
• MPIM: Max Plank Institute for Mathematics
• IRMA: Institut de Recherche Mathe'matique Avance'e
• MFO: Mathematisches Forschungsinstitut Oberwolfach