Related papers: Shadows of mapping class groups: capturing convex …
The moduli space of twisted holomorphic 1-forms on Riemann surfaces, equivalently dilation surfaces with scaling, admits a stratification and GL(2,R)-action as in the case of moduli spaces of translation surfaces. We produce an analogue of…
We show that the mapping class group of a compact orientable surface with higher complexity has the following extreme rigidity in the sense of measure equivalence: if the mapping class group is measure equivalent to a discrete group, then…
Let $S$ be a compact Riemann surface and let $H$ be a finite group. It is known that if $H$ acts on $S$ then there is a $H$-equivariant isogeny decomposition of the Jacobian variety $JS$ of $S,$ called the group algebra decomposition of…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can…
We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…
The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective…
In this article, we derive a sub convexity estimate of Hecke eigen cusp forms associated to certain cocompact arithmetic subgroups of SL(2,R). The main result can be considered as the holomorphic version of the estimate of Hecke eigen Maass…
We describe the mapping class group action on the cohomology of the twisted $\mathrm{SL}_n$-character variety of a surface $\Sigma_g$ of genus $g$. Our main tool is a relative version of the endoscopic decomposition of Maulik-Shen; this…
We compare different notions of limit sets for the action of Kleinian groups on the $n-$dimensional projective space via the irreducible representation $\varrho:PSL(2,\mathbb{C})\to PSL(n+1,\mathbb{C}).$ In particular, we prove that if the…
Hyperelliptic mapping class groups are defined either as the centralizers of hyperelliptic involutions inside mapping class groups of oriented surfaces of finite type or as the inverse images of these centralizers by the natural…
We show that there is a collection of subgroups of the mapping class group of a surface such that the associated coset intersection complex is quasi-isometric and homotopy equivalent to the curve complex. Moreover, we prove that these two…
In this paper, we briefly review some of the known results concerning the cohomological structures of the mapping class group of surfaces, the outer automorphism group of free groups, the diffeomorphism group of surfaces as well as various…
This article uses homological methods for evaluating compactly supported cohomology groups of noncompact toric surfaces
We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…
It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger…
We show that the automorphism group of the complex of pants decompositions for a surface is isomorphic to the mapping class group for that surface.
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
This paper highlights the similarities between even-dimensional geometry (symplectic) and odd-dimensional geometry (cosymplectic). We study the Lagrangian Grassmannian in the cosymplectic setting. The space of compatible co-complex…