相关论文: New series in the Johnson cokernels of the mapping…
We study the cokernel of the Johnson homomorphism for the mapping class group of a surface with one boundary component. A graphical trace map simultaneously generalizing trace maps of Enomoto-Satoh and Conant-Kassabov-Vogtmann is given, and…
In [ES2], the first and the third authors introduced new classes in the Johnson cokernels of the mapping class groups of surfaces by a representation theoretic approach based on some previous results for the Johnson cokernels of the…
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
The degree $d$ part of the cokernel $\mathsf C_d$ of the Johnson homomorphism decomposes into irreducible $\mathrm{SP}$-modules indexed by partitions of $d-2r$ for $r\geq 0$: $$\mathsf C_d\cong \mathsf C_d(d)\oplus \mathsf…
We study stable Sp-decompositions of the cokernel of the Johnson homomorphism. Continuing the work of Conant in 2016, which identified the 1-loop part of the Johnson cokernel as the Enomoto-Satoh obstruction, we study the 2-loop part. Using…
The Johnson kernel is the subgroup $\mathcal{K}_g$ of the mapping class group ${\rm Mod}(\Sigma_{g})$ of a genus $g$ oriented closed surface $\Sigma_{g}$ generated by all Dehn twists about separating curves. In this paper we study the…
In this paper, we study the Johnson homomorphisms of basis-conjugating automorphism groups of free groups. We construct obstructions for the surjectivity of the Johnson homomorphisms. By using it, we determine its cokernels of degree up to…
Let $\Sigma_g \to E \to \Sigma_h$ be a surface bundle over a surface with monodromy representation $\rho: \pi_1 \Sigma_h \to \operatorname{Mod}(\Sigma_g)$ contained in the Torelli group $\mathcal{I}_g$. In this paper we express the cup…
Infinite presentations are given for all of the higher Torelli groups of once-punctured surfaces. In the case of the classical Torelli group, a finite presentation of the corresponding groupoid is also given, and finite presentations of the…
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 a free abelian quotient. In terms of the representation…
For all but finitely many compact orientable surfaces, we show that any superinjective map from the complex of separating curves into itself is induced by an element of the extended mapping class group. We apply this result to proving that…
In this paper we describe the space of maximal components of the character variety of surface group representations into PSp(4,R) and Sp(4,R). For every rank 2 real Lie group of Hermitian type, we construct a mapping class group invariant…
The so-called Johnson homomorphisms $(\tau_k)_{k \geq 1}$ embed the graded space associated to the Johnson filtration of a surface with one boundary component into the Lie ring of positive symplectic derivations $D(H)$. In this paper, we…
This paper is about cohomology of mapping class groups from the perspective of arithmetic groups. For a closed surface $S$ of genus $g$, the mapping class group $Mod(S)$ admits a well-known arithmetic quotient $Mod(S)\rightarrow Sp(2g, Z)$,…
Let K be an algebraically closed field of characteristic p>0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight…
For a compact orientable surface $\Sigma_{g,1}$ of genus $g$ with one boundary component and for an odd prime number $p$, we study the homology of the unordered configuration spaces…
We introduce an embedding of the Torelli group of a compact connected oriented surface with non-empty connected boundary into the completed Kauffman bracket skein algebra of the surface, which gives a new construction of the first Johnson…
Combinatorial aspects of the Torelli-Johnson-Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group…
The action of the mapping class group $\mathrm{Mod}_g$ of an oriented surface $\Sigma_g$ on the lower central series of $\pi_1(\Sigma_g)$ defines the descending filtration in $\mathrm{Mod}_g$ called the Johnson filtration. The first two…
In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various…