Related papers: Non-realizability of some big mapping class groups

We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…

We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and…

In this work we compute the first integral cohomology of the pure mapping class group of a non-orientable surface of infinite topological type and genus at least 3. To this purpose, we also prove several other results already known for…

We show that a homotopy equivalence between two non-compact orientable surfaces is homotopic to a homeomorphism if and only if it preserves the Goldman bracket, provided our surfaces are neither the plane nor the punctured plane.

Let M be a smooth manifold which is homeomorphic to the n-fold product of S^k, where k is odd. There is an induced homomorphism from the group of diffeomorphisms of M to the automorphism group of H k (M ; Z). We prove that the image of this…

We prove a reconstruction theorem for homeomorphism groups of open sets in metrizable locally convex topological vector spaces. We show that certain small subgroups of the full homeomorphism group obey the conditions of the above theorem.

We show that on a compact complex surface all Massey products of cohomology classes in degree one vanish beyond length three. Dually, the real Malcev completion of the fundamental group is homogeneously presented by quadratic and cubic…

We provide new constraints for algebro-geometric subgroups of mapping class groups, namely images of fundamental groups of curves under complex algebraic maps to the moduli space of smooth curves. Specifically, we prove that the restriction…

A $\textit{regular polygon surface}$ $M$ is a surface graph $(\Sigma, \Gamma)$ together with a continuous map $\psi$ from $\Sigma$ into Euclidean 3-space which maps faces to regular Euclidean polygons. When $\Sigma$ is homeomorphic to the…

We give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

We prove that if $\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation…

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.

We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping…

Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

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.…

Let $N$ be a connected nonorientable surface of genus $g$ with $n$ punctures. Suppose that $g$ is odd and $g+n \geqslant 6$. We prove that the automorphism group of the complex of curves of $N$ is isomorphic to the mapping class group…

We study the dynamics of Topologically Anosov homeomorphisms of non compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if $f:S \to S$, is a Topologically Anosov homeomorphism where $S$…

We give a short and elementary proof of the non-realizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of Thurston. With the tools established in this paper, we also…

Let M be a surface (possibly nonorientable) with punctures and/or boundary components. The paper is a study of ``geometric subgroups'' of the mapping class group of M, that is subgroups corresponding to inclusions of subsurfaces (possibly…