# Tagged Questions

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**1**answer

295 views

### Leray Spectral Sequence

Let $f:X\to Y$ be a smooth map between paracompact differential manifolds $X$ and $Y$.
Let $U$ be an open and dense subset of $Y$. For any $y\in U$, let $f^{-1}(y)=F$
be a generic fiber that is a ...

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**2**answers

468 views

### Three half circles on the plane may not meet nicely

Let $H$ denote the union of the northen hemisphere of the unit circle $S^{1}$ with the interval $[-1,1]$ on the $x$-axis. That is, $H=\{(x,\sqrt{1-x^{2}}):-1\le x\le 1\}\cup\{(x,0):-1\le x\le 1\}$
...

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**3**answers

491 views

### Cylinders dividing $\mathbb{R}^{3}$

Consider $n$ affine copies of a compact cylinder, say $S^{1}\times [-3,3]$ with top and botom, sitting inside $\mathbb{R}^{3}$.
For each $n$ we may ask ourselves how to arrange the $n$ cylinders so ...

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**2**answers

451 views

### The “grassmannian” of a simplicial complex

This question is mainly a reference request – I have a construction which seems natural, so I am quite convinced it should be standard, but I don't know what it is called.
Take an $n$ dimensional ...

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**1**answer

1k views

### Good Surface,Bad Surface-Surface classification

Maybe this question be very simple, but I don't know why it is hard for me. Thanks for any guide and help.
We say a surface $S$ (2-dimensional metric(compact) Riemannian surface) is good (denote by ...

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**1**answer

368 views

### Program for drawing cobordisms [closed]

Perhaps this is not the right place to ask the following question but I did not find any suitable on the web. So I would be very grateful for sharing your experience.
What is a good program to draw ...

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**0**answers

304 views

### is a group $G$, that admits finite $k(G, 1)$ and has no Baumslag-Solitar subgroups, necessarily hyperbolic?

This is the first question asked in Bestvina's article "Questions in Geometric Group Theory". Does anyone know if there has been any progress made on this problem? Is the question answered if $G$ is ...

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**1**answer

336 views

### Number of connected components of complement to a reducible real algebraic hypersurface.[EDITED]

Let $X_1,\ldots X_k$ be irreducible(may be singular) affine real algebraic hypersurfaces in $R^n$ with $x_1,\ldots, x_k$ connected components, respectively.
Let $G_1,\ldots, G_l$ be their ...

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**4**answers

563 views

### What is the “right” deifinition of the homology(cohomology) of an orbifold?

What is the "right" analog in the orbifold case of a singular homology of a topological space?
We can not just take the homology of the underlying space, because it does not contain much imformation.
...

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**2**answers

782 views

### Mathematics of Doodling and the Winding Number

So I was reading the American Mathematical Monthly Feb 2011 (Volume 118, number 2), and in particular, I was interested in Ravi Vakil's article about mathematics of doodling. There is a question I ...

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**0**answers

127 views

### System dynamic of space euclidean and hyperbolic tilings

Theorem 2.9. (Rudolph [Rud89]) Suppose $X_{T}$ is a finite local complexity (FLC)
tiling space. Then $X_{T}$ is compact in the tiling metric d. Moreover, the action $T$ of
$R^{d}$ by translation is on ...

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**1**answer

397 views

### Generalization of Moise's theorem

I am looking for a generalization of Moise's theorem, which the few professors that I asked treat as a "known geometric fact" but none could find a reference to an article proving it.
The claim is ...

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**8**answers

3k views

### The Symmetry of a Soccer Ball

Let $P$ be a polyhedron which satisfies the following three conditions:
$P$ is built out of regular hexagons and regular pentagons.
Three faces meet at each vertex.
$P$ is topologically a sphere.
...

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**4**answers

679 views

### Geometry of the multilagrangian Grassmannian

Let's introduce the following variety $MG(3,6)$, which is a "multisymplectic" analog of a Lagrangian Grassmannian $LG(3,6)$.
Consider a 3-form $\omega = dx1 \wedge dx2 \wedge dx^3 - dx4 \wedge dx5 ...