On Meyer's function of hyperelliptic mapping class groups

Automorphism groups of hyperelliptic function fields

On Endomorphisms of Surface Mapping Class Groups

We prove in this paper that every endomorphism of the mapping class group of certain orientable surfaces onto a subgroup of finite index is in fact an automorphism.

Mapping Class Groups

2 Topology of surfaces 5 2.1 The dimension 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Classi cation of surfaces . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Circles and arcs on surfaces . . . . . . . . . . . . . . . . . . . . . 7 2.4 Pants decompositions . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Geometric structures on surfaces . . . . . . . . . . . . . . ....

Galois Action on Mapping Class Groups

Let l be a prime number. In this present paper, we study the outer Galois action on the profinite and the relative pro-l completions of mapping class groups of pointed orientable topological surfaces. In the profinite case, we prove that the outer Galois action is faithful. In the pro-l case, we prove that the kernel of the outer Galois action has certain stability properties with respect to th...

Quasi-homomorphisms on Mapping Class Groups

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasihomomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarge the class of such subgroups. The generalization is motivated by consideratio...