Related papers: Spaces over BO are thickened manifolds

A classical result of A.D. Alexandrov states that a connected compact smooth $n-$dimensional manifold without boundary, embedded in $\Bbb R^{n+1}$, and such that its mean curvature is constant, is a sphere. Here we study the problem of…

We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free…

We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…

Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the…

The group of direct isometries of the real n-dimensional hyperbolic space is G=SOo(n,1). This isometric action admits many differentiable compactifications into an action on the closed ball. We prove that all such compactifications are…

We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…

Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic…

We prove that the algebra of singular cochains on a smooth manifold, equipped with the cup product, is equivalent to the A-infinity structure on the Lagrangian Floer cochain group associated to the zero section in the cotangent bundle. More…

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…

We show that there are homotopy equivalences $h:N\to M$ between closed manifolds which are induced by cell-like maps $p:N\to X$ and $q:M\to X$ but which are not homotopic to homeomorphisms. The phenomenon is based on construction of…

In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a $1/4-$pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That…

We show that large classes of non-arithmetic hyperbolic $n$-manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only finitely many finite-volume immersed totally geodesic…

We consider the topological category of $h$-cobordisms between manifolds with boundary and compare its homotopy type with the standard $h$-cobordism space of a compact smooth manifold.

We prove that every visual Gromov hyperbolic space X whose boundary at infinity has the finite capacity dimension n admits a quasi-isometric embedding into (n+1)-fold product of metric trees.

Let k>2. We prove that the cotangent bundles of oriented homotopy (2k-1)-spheres S and S' are symplectomorphic only if the classes defined by S and S' agree up to sign in the quotient group of oriented homotopy spheres modulo those which…

It is shown that any smooth closed orientable manifold of dimension $2k + 1$, $k \geq 2$, admits a smooth polynomially convex embedding into $\mathbb C^{3k}$. This improves by $1$ the previously known lower bound of $3k+1$ on the possible…

We show that the category of truncated spaces with finite homotopy invariants ($\pi$\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the natural higher analogue of the elementary…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…