Related papers: Exotic projective structures and quasifuchsian spa…

We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a closed, connected, and oriented Riemannian $n$-manifold, and…

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each…

We study the pants complex of surfaces of infinite type. When $S$ is a surface of infinite type, the usual definition of the pants graph $\mathcal{P}(S)$ yields a graph with infinitely many connected-components. In the first part of our…

The non-abelian Hodge correspondence maps a polystable $\mathrm{SL}(2,\mathbb{R})$-Higgs bundle on a compact Riemann surface $X$ of genus $g\geq2$ to a connection which, in some cases, is the holonomy of a branched hyperbolic structure. On…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…

We prove that there exist hypersurfaces that contain a given closed subscheme $Z$ of the projective space over a finite field and intersect a given smooth scheme $X$ off of $Z$ smoothly, if the intersection $V = Z \cap X$ is smooth.…

We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact…

In this paper, we will determine the topological types of hyperbolic 3-anifolds H^3/G such that G is a geometric limit of any algebraically convergent sequence of quasi-Fuchsian groups.

We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples…

We show the existence of infinitely many knot exteriors where each of which contains meridional essential surfaces of any genus and (even) number of boundary components. That is, the compact surfaces that have a meridional essential…

Let $\Sigma$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $\Sigma$, possibly with opposite orientations. In this paper, we show that there are (exactly) countably…

Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…

For a boundary-reducible $3$-manifold $M$ with $\partial M$ a genus $g$ surface, we show that if $M$ admits a genus $g+1$ Heegaard surface $S$, then the disk complex of $S$ is simply connected. Also we consider the connectedness of the…

We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain related manifolds. These structures occur in bouquets and exhaust the Sasaki cones…

The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…

We show that there are no non-trivial stratified bundles over a smooth simply connected quasi-projective variety over the algebraic closure of a finite field, if the variety admits a normal projective compactification with boundary locus of…

The goal of the article is to characterize the conservative homeomorphisms of a closed orientable surface $S$ of genus $\geq 2$, that have finitely many periodic points. By conservative, we mean a map with no wandering point. As a…

In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex…

Let $S$ be a closed orientable surface of genus at least two. We introduce a bordification of the moduli space $\mathcal{PT}(S)$ of complex projective structures, with a boundary consisting of projective classes of half-translation…

For every proper geodesic space $X$ we introduce its quasi-geometric boundary $\partial_{QG}X$ with the following properties: 1. Every geodesic ray $g$ in $X$ converges to a point of the boundary $\partial_{QG}X$ and for every point $p$ in…