Related papers: Monodromy kernels for strata of translation surfac…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold,…

The {\em Prym} of a cyclic covering of smooth projective curves is the ``new'' part of the Jacobian: the quotient of the Jacobian of the covering curve by the Jacobians of the intermediate covers. Given a family of such coverings, the…

In this paper, we construct H\"older maps to Carnot groups equipped with a Carnot metric, especially the first Heisenberg group $\mathbb{H}$. Pansu and Gromov observed that any surface embedded in $\mathbb{H}$ has Hausdorff dimension at…

We study the kernels of representations of mapping class groups of surfaces on twisted homologies of configuration spaces. We relate them with the kernel of a natural twisted intersection pairing: if the latter kernel is trivial then the…

Let $\mathscr{C}$ be a symmetric tensor category of moderate growth, and let $\mathcal{H}\subseteq\mathcal{G}$ be algebraic groups in $\mathscr{C}$. We prove that the homogeneous space $\mathcal{G}/\mathcal{H}$ exists and is of finite type…

We compute the Z/\ell and \ell-adic monodromy of every irreducible component of the moduli space M_g^f of curves of genus and and p-rank f. In particular, we prove that the Z/\ell-monodromy of every component of M_g^f is the symplectic…

The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. We prove a Birman exact…

We consider autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. We prove that the image of the autoequivalences has index at most two in the group of the Hodge isometries of the Mukai lattice. Motivated by…

We study algebraic structures of certain submonoids of the monoid of homology cylinders over a surface and the homology cobordism groups, using Reidemeister torsion with non-commutative coefficients. The submonoids consist of ones whose…

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely,…

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our…

Let $k$ be a number field and $B$ be a central simple algebra over $k$ of dimension $p^2$ where $p$ is prime. In the case that $p=2$ we assume that $B$ is not totally definite. In this paper we study sets of pairwise nonisomorphic maximal…

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the…

Over the complex numbers, the complement of a collection of hyperplanes is a widely-studied object; the cohomology ring, in particular, is known to have a structure depending only on the combinatorial properties of the intersection of…

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…

We prove that many normal subgroups of the extended mapping class group of a surface with punctures are geometric, that is, that their automorphism groups and abstract commensurator groups are isomorphic to the extended mapping class group.…

The aim of this thesis is to study under which conditions $K3$ surfaces allowing a triple-point-free model satisfy the monodromy property. This property is a quantitative relation between the geometry of the degeneration of a Calabi-Yau…

Let $H_n$ be the $n$-th group homology functor (with integer coeffcients) and let $\{G_i\} _ {i \in \mathbb{N}}$ be any tower of groups such that all maps $G_{i+1} \to G_i$ are surjective. In this work we study kernel and cokernel of the…

We prove that if a normal subgroup of the extended mapping class group of a closed surface has an element of sufficiently small support then its automorphism group and abstract commensurator group are both isomorphic to the extended mapping…