Related papers: Affine deformations of a three-holed sphere

This article provides, over any field, infinitely many algebraic embeddings of the affine spaces $\mathbb{A}^1$ and $\mathbb{A}^2$ into smooth quadrics of dimension two and three respectively, which are pairwise non-equivalent under…

In [LMO] a 3-manifold invariant $\Omega(M)$ is constructed using a modification of the Kontsevich integral and the Kirby calculus. The invariant $\Omega$ takes values in a graded Hopf algebra of Feynman 3-valent graphs. Here we show that…

Let $(M, \partial M)$ be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric $g$ on $M$ such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$…

An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant…

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

If M is a closed simple 3-manifold whose fundamental group contains a genus-g surface group for some g>1, and if the dimension of H_1(M;Z_2) is at least max(3g-1,6), we show that M contains a closed, incompressible surface of genus at most…

We prove that any compact, orientable 3-manifold with empty or toral boundary is profinitely almost rigid among all compact, orientable 3-manifolds. In other words, the profinite completion of its fundamental group determines its…

Let $M$ be a closed, orientable hyperbolic 3-manifold and $\phi$ a homomorphism of its fundamental group onto $\mathbb{Z}$ that is not induced by a fibration over the circle. For each natural number $n$ we give an explicit lower bound,…

We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.

Let $X$ denote a metric Lie group diffeomorphic to $\mathbb{R}^3$ that admits an algebraic open book decomposition. In this paper we prove that if $\Sigma$ is an immersed surface in $X$ whose left invariant Gauss map is a diffeomorphism…

This paper proves that every finite volume hyperbolic 3-manifold M contains a ubiquitous collection of closed, immersed, quasi-Fuchsian surfaces. These surfaces are ubiquitous in the sense that their preimages in the universal cover…

It was recently shown that under mild assumptions second-order conformally superintegrable systems can be encoded in a $(0,3)$-tensor, called structure tensor. For abundant systems, this approach led to algebraic integrability conditions…

An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. Equivalently an affine $3$-manifold is a $3$-manifold…

For a given smooth $2$-knot in $S^4$, we relate the existence of a smooth Seifert hypersurface of a certain class to the existence of irreducible $ SU(2)$-representations of its knot group. For example, we see that any smooth $2$-knot…

It has been recently shown by Abresch and Rosenberg that a certain Hopf differential is holomorphic on every constant mean curvature surface in a Riemannian homogeneous 3-manifold with isometry group of dimension 4. In this paper we…

We construct compact hyperbolic 3-manifolds with totally geodesic boundary, such that the closed 3-pseudomanifolds obtained by coning off the boundary components are negatively curved and contain locally convex subspaces whose fundamental…

This note studies the Burnside problem for homeomorphism groups of compact connected manifolds. For surfaces, we prove that the identity component of the homeomorphism group is torsion-free precisely when the surface is not the sphere,…

Let M be a closed 5-manifold of pinched curvature 0<\delta\le \text{sec}_M\le 1. We prove that M is homeomorphic to a spherical space form if M satisfies one of the following conditions: (i) \delta =1/4 and the fundamental group is a…

In this paper we study embeddings of oriented connected closed surfaces in $\mathbb S^3$. We define a complete invariant, the fundamental span, for such embeddings, generalizing the notion of the peripheral system of a knot group. From the…

We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…