Homepage of Takuya SAKASAI
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 +)
Workshops
Research Interests
Topology, Mapping class groups of surfaces, Characteristic classes of bundles, Graph homology,
Moduli spaces of Riemann surfaces, Moduli spaces of metric graphs, Supermanifolds,
3-dimensional 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), 83-111.
-
Homology cylinders and the acyclic closure of a free group.
Algebraic &
Geometric Topology 6 (2006), 603-631.
-
The second Johnson homomorphism and the second rational cohomology
of the Johnson kernel.
Mathematical Proceedings of the Cambridge
Philosophical Society 143 (2007), 627-648.
-
The symplecticity of the Magnus representation for homology cobordisms
of surfaces.
Bulletin of the Australian Mathematical Society 76 (2007), 421-431.
-
The Magnus representation and higher-order Alexander invariants
for homology cobordisms of surfaces.
Algebraic &
Geometric Topology 8 (2008), 803-848.
- (With Hiroshi Goda)
Abelian quotients of monoids of homology cylinders.
Geometriae Dedicata 151 (2011), 387-396.
- (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.
- Lagrangian mapping class groups from a group homological point of view.
Algebraic &
Geometric Topology 12 (2012), 267-291.
- (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.
- (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.
- (With Shigeyuki Morita and Masaaki Suzuki)
Integral Euler characteristic of Out F_{11}.
Experimental Mathematics
24, (2015), 93-97.
- (With Shigeyuki Morita and Masaaki Suzuki)
Computations in formal symplectic geometry and characteristic classes of moduli spaces.
Quantum Topology 6 (2015), 139-182.
- The Magnus representation and homology cobordism groups of homology cylinders.
Journal of Mathematical Sciences, the University of Tokyo 22 (2015), 741-770.
- (With Shigeyuki Morita and Masaaki Suzuki)
Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras.
Advances in Mathematics
282 (2015), 291-334.
- (With Shigeyuki Morita and Masaaki Suzuki)
Symmetry of symplectic derivation Lie algebras of free Lie algebras.
RIMS Kôkyûroku Bessatsu B66 (2017), 185-193.
- (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.
- (With Shigeyuki Morita and Masaaki Suzuki)
Torelli group, Johnson kernel and invariants of homology spheres.
Quantum Topology 11 (2020), 379-410.
- (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
- Higher-order Alexander invariants for homology cobordisms
of a surface.
Intelligence of Low Dimensional Topology 2006,
Series on Knots and Everything 40, 271-278.
- 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.
-
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.
-
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.
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).
Dissertation
- 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 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