# Tagged Questions

**3**

votes

**1**answer

144 views

### Triangulation of the surface determined by sampling two of its cross-sections

I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in principle I do not ...

**9**

votes

**2**answers

522 views

### Discrete Morse function from smooth one

Suppose I have a smooth manifold $M$ and a smooth Morse function $f$ on $M$. Is there a standard way to replace $M$ with a cell complex and $f$ with a discrete Morse function such the resulting ...

**3**

votes

**0**answers

235 views

### Coloring $\mathbb{Z}^k$ and a fixed point theorem

This is potentially another approach to this question. I put it as an update there, but perhaps it would be better to post it separately. If we color $\mathbb{Z}^k$ with the $\ell_\infty$ metric in ...

**1**

vote

**1**answer

620 views

### Applications of ham sandwich type results. References? A general principle?

Lately there has been a lot of interest on applications of the ham sandwich theorem and related results. There is a bunch of lecture notes and surveys that touch upon the subject. I dont know of any ...

**9**

votes

**1**answer

730 views

### A Desirable Extension of the Nerve Theorem

Backgroud
The Nerve Theorem (see nLab;) asserts that given a finite collection $\cal K$ of compact sets with the property that all non empty intersections of sets in the family are homotopically ...

**6**

votes

**0**answers

256 views

### A question about a blue fan and a red fan and their common refinement

Is the following conjecture true?
Conjecture: Let $M_1$ be a red map and let $M_2$ be a blue map drawn in general position on $S^n$, and let $M$ be their common refinement. There is a vertex $w$ of ...

**15**

votes

**0**answers

1k views

### Covers of $Z^k$

This is a question related to covers of $Z^\infty$. Is it possible to cover $Z^k$, $k>1$, with the $l_1$-metric by a constant (not depending on $k$) number of collections of subsets $U^0,...,U^c$ ...

**11**

votes

**2**answers

710 views

### covers of $Z^\infty$

Is it possible to cover $Z^\infty$ (the infinite direct sum of $Z$'s with the $l_1$-metric) by a finite set of collections of subsets $U^0,...,U^n$ such that each collection $U^i$ consists of ...