Related papers: Affine deformations of a three-holed sphere

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

The group action which defines the moduli problem for the deformation space of flat affine structures on the two-torus is the action of the affine group $\Aff(2)$ on $\bbR^2$. Since this action has non-compact stabiliser $\GL(2,\bbR)$, the…

An automorphism $f$ of a closed orientable surface $\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma)$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove…

For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the…

Let $M$ be a convex body and let $K$ be a closed convex surface $K$ both contained in the Euclidean space $\mathbb{E}^3$. What can we say about $M$ if $K$ encloses $M$ and if from all the points in $K$ the body $M$ looks the same? In this…

We give necessary and sufficient conditions for an affine deformation of a Schottky subgroup of O(2,1) to act properly on affine space. There exists a real-valued biaffine map between the cohomology of the Schottky group and the space of…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positve integral multiple represented by an…

Starting with an O(2)-principal fibration over a closed oriented surface F_g, g>=1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) = S^1 to the nontrivial element of Z_2. Adapting D…

We prove that if S is a properly embedded incompressible surface in a compact 3-manifold M, then the fundamental group of S is separable in the fundamental group of M.

Every closed orientable surface S has the following property: any two connected covers of S of the same degree are homeomorphic (as spaces). In this, paper we give a complete classification of compact 3-manifolds with empty or toroidal…

We show that every closed, virtually fibered hyperbolic 3-manifold contains immersed, quasi-Fuchsian surfaces with convex cores of arbitrarily large thickness.

We show that if $M$ is an Einstein hypersurface in an irreducible Riemannian symmetric space $\overline{M}$ of rank greater than $1$ (the classification in the rank-one case was previously known), then either $\overline{M}$ is of noncompact…

Let $ M^{n+1} $ ($ n \ge 2 $) be a simply-connected space form of sectional curvature $ -\kappa^2 $ for some $ \kappa \geq 0 $, and $ I $ an interval not containing $ [-\kappa,\kappa] $ in its interior. It is known that the domain of a…

We find that for any n-dimensional, compact, convex subset K of R^{n+1} there is an affinely-spherical hypersurface M in R^{n+1} with center at the relative interior of K, such that the disjoint union of M and K is the boundary of an…

In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to…

According to the Markus conjecture, closed flat affine manifolds with parallel volume should be complete. We show it is the case for three-manifolds when the holonomy centralizes an affine transformation preserving the volume. It is notably…

Hildebrand classified all semi-homogeneous cones in $\mathbb{R}^3$ and computed their corresponding complete hyperbolic affine spheres. We compute isothermal parametrizations for Hildebrand's new examples. After giving their affine metrics…

A filling Dehn sphere $\Sigma$ in a closed 3-manifold $M$ is a sphere transversely immersed in $M$ that defines a cell decomposition of $M$. Every closed 3-manifold has a filling Dehn sphere. The Montesinos complexity of a $3$-manifold $M$…

We study complete finite topology immersed surfaces $\Sigma$ in complete Riemannian $3$-manifolds $N$ with sectional curvature $K_N\leq -a^2\leq 0$, such that the absolute mean curvature function of $\Sigma$ is bounded from above by $a$ and…