Related papers: Automorphisms of Torelli groups
In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…
For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…
In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…
We give a new proof of the theorem of Birman-Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key…
We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
Recently Bowden, Hensel and Webb defined the fine curve graph for surfaces, extending the notion of curve graphs for the study of homeomorphism or diffeomorphism groups of surfaces. Later Long, Margalit, Pham, Verberne and Yao proved that…
Let $S$ be a nonorientable surface of genus $g\ge 5$ with $n\ge 0$ punctures, and $\Mcg(S)$ its mapping class group. We define the complexity of $S$ to be the maximum rank of a free abelian subgroup of $\Mcg(S)$. Suppose that $S_1$ and…
Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group…
Building on work of Farb and the second author, we prove that the group of automorphisms of the fine curve graph for a surface is isomorphic to the group of homeomorphisms of the surface. This theorem is analogous to the seminal result of…
Using a refinement of the differential method introduced by Oguiso and Yu, we provide effective conditions under which the automorphisms of a smooth degree $d$ hypersurface of $\mathbf{P}^{n+1}$ are given by generalized triangular matrices.…
The fine curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consisting of essential simple closed curves on the surface. Long, Margalit, Pham, Verberne, and Yao proved that the automorphism group of the fine…
We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…
By Torelli topology the author understands aspects of the topology of surfaces (potentially) relevant to the study of Torelli groups. The extension problem in Torelli topology is the problem of determining when a diffeomorphism of compact…
We show that any isomorphism between mapping class groups of orientable infinite-type surfaces is induced by a homeomorphism between the surfaces. Our argument additionally applies to automorphisms between finite-index subgroups of these…
In this paper, we consider the automorphisms of fine curve graphs restricted to continuously $k$-differentiable curves. We show that for closed surfaces with genus at least 2, they are induced by homeomorphisms of the surface.
We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…
We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be…
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…
This paper shows that the automorphism group of a Beauville surface is a finite solvable group, and describes its possible structure. It relies on results of Singerman on triangle group inclusions, and of Lucchini on generators for special…
In this note we show that if the automorphism group of a normal affine surface $S$ is isomorphic to the automorphism group of a Danielewski surface, then $S$ is isomorphic to a Danielewski surface.