Homepage of Takuya SAKASAI
Takuya SAKASAI
Associate Professor
Graduate School of Mathematical Sciences,
The University of Tokyo,
381 Komaba Meguroku Tokyo 1538914, Japan.
Email address: sakasai + @ms.utokyo.ac.jp
(Please remove +)
Workshops
Research Interests
Topology, mapping class groups of surfaces, characteristic classes of bundles, graph homology,
3dimensional manifolds, homology cobordisms, noncommutative algebra etc...
Papers
 The Johnson homomorphism and the third rational cohomology group
of the Torelli group.
Topology and its Applications 148 (2005), 83111.

Homology cylinders and the acyclic closure of a free group.
Algebraic &
Geometric Topology 6 (2006), 603631.

The second Johnson homomorphism and the second rational cohomology
of the Johnson kernel.
Mathematical Proceedings of the Cambridge
Philosophical Society 143 (2007), 627648.

The symplecticity of the Magnus representation for homology cobordisms
of surfaces.
Bulletin of the Australian Mathematical Society 76 (2007), 421431.

The Magnus representation and higherorder Alexander invariants
for homology cobordisms of surfaces.
Algebraic &
Geometric Topology 8 (2008), 803848.
 (With Hiroshi Goda)
Abelian quotients of monoids of homology cylinders.
Geometriae Dedicata 151 (2011), 387396.
 (With Hiroshi Goda)
Factorization formulas and computations of higherorder Alexander invariants
for homologically fibered knots.
Journal of Knot Theory and Its Ramifications 20 (2011), 13551380.
 Lagrangian mapping class groups from a group homological point of view.
Algebraic &
Geometric Topology 12 (2012), 267291.
 (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), 85111.
 (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), 9651002.
 (With Shigeyuki Morita and Masaaki Suzuki)
Integral Euler characteristic of Out F_{11}.
Experimental Mathematics
24, (2015), 9397.
 (With Shigeyuki Morita and Masaaki Suzuki)
Computations in formal symplectic geometry and characteristic classes of moduli spaces.
Quantum Topology 6 (2015), 139182.
 The Magnus representation and homology cobordism groups of homology cylinders.
Journal of Mathematical Sciences, the University of Tokyo 22 (2015), 741770.
 (With Shigeyuki Morita and Masaaki Suzuki)
Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras.
Advances in Mathematics
282 (2015), 291334.
 (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).
 (With Shigeyuki Morita and Masaaki Suzuki)
Symmetry of symplectic derivation Lie algebras of free Lie algebras.
RIMS Kôkyûroku Bessatsu B66 (2017), 185193.
 (With Gwénaël Massuyeau)
Morita's trace maps on the group of homology cobordisms.
To appear in Journal of Topology and Analysis,
arXiv:math.GT/1606.08244, (19 Sep 2018).
Proceedings and Surveys
 Higherorder Alexander invariants for homology cobordisms
of a surface.
Intelligence of Low Dimensional Topology 2006,
Series on Knots and Everything 40, 271278.
 Johnson's homomorphisms and the rational cohomology of
subgroups of the mapping class group.
Groups of Diffeomorphisms,
Advanced studies in pure mathematics 52, (2008), 93109.

A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces.
Handbook of Teichmüller theory volume III (editor: A. Papadopoulos), (2012), 531594.

JohnsonMorita theory in mapping class groups and monoids of homology cobordisms of surfaces.
Winter Braids Lecture Notes 3, (2016), Course no IV 125.
Preprints
 (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).
 (With Shigeyuki Morita and Masaaki Suzuki)
Torelli group, Johnson kernel and invariants of homology spheres.
arXiv:math.GT/1711.07855, (22 Nov 2017).
Dissertation
 Mapping class groups, groups of homology cobordisms of surfaces
and invariants of 3manifolds.
Doctoral Dissertation, The University of Tokyo, 2006.
Almost all of the contents were published in the papers 1,2,3,5 and the survey paper 3.
T4M7 (Teruaki for Mathematica 7)
 "T4M7" 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 7) is a joint work with Masaaki Suzuki.
 T4M7 download: [manual (please read first)],
[closed surface version],
[surface with boundary version].
Links