22 citations · 130 across the 19 of their papers we have counts for
19 papers
The first Galois obstruction in the Johnson cokernel
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We explicitly determine the first Galois obstruction in the cokernel of the Johnson homomorphism of the mapping class group of a surface of genus , for every genus . It…
Torelli group, Johnson kernel and invariants of homology spheres
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
In the late 1980's, it was shown that the Casson invariant appears in the difference between the two filtrations of the Torelli group: the lower central series and the Johnson filt…
An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We construct an abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra generated by the fundamental representation of $\mathrm{Sp}(2…
Morita's trace maps on the group of homology cobordisms
Gwenael Massuyeau, Takuya Sakasai
Morita introduced in 2008 a 1-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His 1-cocycle contains all the "traces" o…
Secondary characteristic classes for subgroups of automorphism groups of free groups
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
By analyzing how the Borel regulator classes vanish on various groups related to , we define three series of secondary characteristic classes for subgrou…
Integral Euler characteristic of Out F_{11}
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We show that the integral Euler characteristic of the outer automorphism group of the free group of rank 11 is -1202.
Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We study the structure of the symplectic invariant part of the Lie algebra consisting of symplectic derivations of the free…
Computations in formal symplectic geometry and characteristic classes of moduli spaces
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative on…
Symmetry of symplectic derivation Lie algebras of free Lie algebras
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the firs…
The Magnus representation and homology cobordism groups of homology cylinders
Takuya Sakasai
A homology cylinder over a compact manifold is a homology cobordism between two copies of the manifold together with a boundary parametrization. We study abelian quotients of the h…
Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra
Shigeyuki Morita, Takuya Sakasai, Masaaki Suzuki
We determine the abelianizations of the following three kinds of graded Lie algebras in certain stable ranges: derivations of the free associative algebra, derivations of the free…
A survey of Magnus representations for mapping class groups and homology cobordisms of surfaces
Takuya Sakasai
This is a survey of Magnus representations with particular emphasis on their applications to mapping class groups and monoids (groups) of homology cobordisms of surfaces. In the fi…
Factorization formulas and computations of higher-order Alexander invariants for homologically fibered knots
Hiroshi Goda, Takuya Sakasai
Homologically fibered knots are knots whose exteriors satisfy the same homological conditions as fibered knots. In our previous paper, we observed that for such a knot, higher-orde…
Lagrangian mapping class groups from a group homological point of view
Takuya Sakasai
We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups…
Abelian quotients of monoids of homology cylinders
Hiroshi Goda, Takuya Sakasai
A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylin…
Homology cylinders and sutured manifolds for homologically fibered knots
Hiroshi Goda, Takuya Sakasai
Sutured manifolds defined by Gabai are useful in the geometrical study of knots and 3-dimensional manifolds. On the other hand, homology cylinders are in an important position in t…
The second Johnson homomorphism and the second rational cohomology of the Johnson kernel
Takuya Sakasai
The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as…
The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces
Takuya Sakasai
The set of homology cobordisms from a surface to itself with markings of their boundaries has a natural monoid structure. To investigate the structure of this monoid, we define and…
Homology cylinders and the acyclic closure of a free group
Takuya Sakasai
We give a Dehn-Nielsen type theorem for the homology cobordism group of homology cylinders by considering its action on the acyclic closure, which was defined by Levine, of a free…