Related papers: Automorphisms of Torelli groups
In [I. Arzhantsev and M. Zaidenberg, Acyclic curves and group actions on affine toric surfaces. Affine Algebraic Geometry, 1--41. World Scientific Publishing Co. 2013] we described the automorphism groups of the cyclic quotients of the…
We study the arc complex of a surface with marked points in the interior and on the boundary. We prove that the isomorphism type of the arc complex determines the topology of the underlying surface, and that in all but a few cases every…
We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such…
The theta characteristics on a Riemann surface are permuted by the induced action of the automorphism group, with the orbit structure being important for the geometry of the curve and associated manifolds. We describe two new methods for…
It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the…
We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…
The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.
We show that no finite index subgroup of a sufficiently complicated mapping class group or braid group can act faithfully by $C^{1+\mathrm{bv}}$ diffeomorphisms on the circle, which generalizes a result of Farb-Franks, and which parallels a…
We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.
We compute the automorphisms groups of all numerical Godeaux surfaces, i.e. minimal smooth surfaces of general type with K^2 = 1 and p_g = 0, with torsion of the Picard group of order \nu equals 3, 4, or 5. We present explicit…
We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…
In 2013 Bazhov proved a criterium for two points on a complete toric variety to lie in the same orbit of the neutral component of automorphism group. This criterium is in terms of divisor class group. Arzhantsev-Bazhov (2013) obtained a…
We show that the Torelli group of a closed surface of genus $\ge 3$ acts nontrivially on the rational cohomology of its space of $3$-element subsets.
Recently, Gareth Jones observed that every finite group $G$ can be realized as the group of automorphisms of some dessin d'enfant ${\mathcal D}$. In this paper, complementing Gareth's result, we prove that for every possible action of $G$…
We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general…
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…
The so-called Tits class, associated to an adjoint absolutely almost simple algebraic group, provides a cohomological obstruction for this group to admit an outer automorphism. If the group has inner type, this obstruction is the only one.…
Examples of aspherical closed symplectic 4-manifolds are presented whose Sullivan minimal models are (1,n)-formal for any n, without being formal. They have as cohomology algebra, signature, canonical class, those of a product of a closed…
We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…
We show that every auto-homeomorphism of the unmeasured lamination space of an orientable surface of finite type is induced by a unique extended mapping class unless the surface is a sphere with at most four punctures or a torus with at…