# Tagged Questions

227 views

### diameter as a Morse function

Consider the space $X_1$ of closed subsets not containing a pair of antipodal points of the unit circle. Here we have a kind of degenerate Morse function, defined by the diameter of the pointset. ...
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### Problem on infinite dimensional metric space, with rigidity assumption

By inspiring from this answer of S. Ivanov, here is a specialization with a rigidity assumption. Let $(X_{n},d_{n})_{n \in \mathbb{N}}$ be a sequence of complete geodesic metric spaces verifying : ...
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### Twisted calibrations and sufficient conditions on homology of sub-manifolds

I think my question is somehow easy to solve, but I'm not very familiar with algebraic topology, so I'm not able to figure out the solution for myself. I'm working on a problem in metric geometry and ...
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### Normal tubular neighborhood theorem for semi(or pseudo)-riemannian manifolds

Suppose you have a manifold $M$ and a closed sub-manifold $A$, and let $g$ be a semi-riemannian metric,ie, $g_x$ defines a quadratic form on $T_xM$ such that $g_x(v,v)\ge0$, but $g_x(v,v)=0$ not ...
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### A problem on infinite dimensional metric space

Let $(X_{n},d_{n})_{n \in \mathbb{N}}$ be a sequence of complete geodesic metric spaces verifying : $X_{n}$ is a regular CW complex of constant local dimension $n$. $X_{n}$ is of finite type, ...
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### Are characteristic maps of CW complexes Lipschitz up to homotopy?

Let us consider a finite CW complex $X=\cup X_j$ with a given metric, compatible with the topology (maybe a reasonable one coming from some embedding into some $\mathbb{R}^n$). The characteristic ...
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### Uniquely geodesic and CAT(0) spaces?

Improvement after J-M Schlenker's comment below : This post has been divided into two parts, the second part is here. Question : Is a finite dimensional metric space, uniquely geodesic if and only ...
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### Homotopy problem for infinite dimensional topological space II

This post here is a specification of this post. Let $(X_{n},d_{n})_{n \in \mathbb{N}}$ be a sequence of intrinsic metric spaces verifying : $X_{n}$ have topological dimension $n$. $X_{n+1}$ is ...
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### Systoles of hyperbolic (Riemann) surfaces of large genus

Let $m$ be a Riemannian metric on $S_g$ the surface of genus $g$, and $sys(m)$ be the length of the shortest non contractible cycle with respect to $m$. The systolic inequality claims that for any ...
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### simplicial complex equipped with barycenric metric is complete [closed]

Consider a simplicial complex $C$. On its support |C|=\lbrace \alpha = \sum_{v\in C}\alpha_{v}v \mid 0\leq \alpha_{v} \leq 1 , \sum_{v\in C}\alpha_{v} =1\mbox{ and }v|{\alpha_{v}} \neq 0\mbox{ is a ...
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### Every continuous function is homotopic to a locally Lipschitz one

I would like to know for which category/class/set of metric spaces the following holds: for any two metric spaces $X$, $Y$, for any continuous function $f:X\to Y$ there exists a locally Lipschitz ...
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### A Existence Problem of (p,q) metric

My question is: Can we judge a manifold that can admit a (p,q) metric? I only know the case that the existen of a lorentz metric is equivalent to Euler Character is zero