Related papers: Contractbility of Outer space: reprise
Forester has defined spaces of simplicial tree actions for a finitely generated group, called deformation spaces. Culler and Vogtmann's Outer space is an example of a deformation space. Using ideas from Skora's proof of the contractibility…
We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)
We prove that a contractible orbifold is a manifold.
Let $\cal R$ be an ordered vector space over an ordered division ring. We prove that every definable set $X$ is a finite union of relatively open definable subsets which are definably simply-connected, settling a conjecture from [5]. The…
This paper presents some partial answers to the following question. QUESTION. If a normal space X is the union of an increasing sequence of open sets U(1), U(2), U(3) ... such that each U(n) contracts to a point in X, must X be…
This paper describes a scheme, through which the quantum information as well as the structural information of a time-reversal invariant system can be teleported over a distance. I show that my teleportation scheme can be viewed as a form of…
We give a simple proof that the orbit space of the $p$-subgroup complex of a finite group is contractible using Brown-Forman discrete Morse theory. This result was originally conjectured by Webb and proved by Symonds.
In this note, we show that the space of all $\varepsilon$-nets in the real line $\mathbb{R}$ with a natural metric, equipped with either Hausdorff or Gromov--Hausdorff distance, is contractible.
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
The purpose of this paper is to demonstrate that it is possible, in principle, to obtain knowledge of the entire universe at the present time, even if the radius of the universe is much larger than the radius of the observable universe.
We give a short proof that the Yoneda embedding is natural for $\infty$-categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embedding, is contractible.
Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering…
We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more…
We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to…
This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.
Alternative proof is given for an earlier presented result that if a link in 3-space bounds a compact oriented proper surface (without closed component) in the upper half 4-space, then the link bounds a ribbon surface in the upper half…
This paper has been withdrawn because the part concerning the definition of global hyperbolicity has already been included in an expanded and clearer way in gr-qc/0611138. The remainder will be also extended and posted.
We examine how the consequences which follow from a recent model, both in cosmology and at the elementary particle level have since been observationally and experimentally confirmed. Some of the considerations of the model are also…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this note we establish two facts concerning the so-called {\em New-Jersey} outer bound. We show that this outer bound is equivalent to a much simpler {\em computable} region; and secondly we show that in the absence of private…