# Tagged Questions

0answers
35 views

### References on the relations between Top, Diff and PL

I have heard many times informal statements like "differentiable and pl manifolds are essentially the same for such and such dimensions", but I would like to know what they mean exactly and how such ...
1answer
168 views

### Russian Texts on Geometry

I recently saw a question today pertaining to Russian mathematics and I have a similar question but of a slightly different flavor. I've always heard that the Soviet Union had a history of producing ...
0answers
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### Actual Definition of the term: Hopf Band?

Sorry if this is too trivial: I need an actual working definition of the term: Hopf band. I see references to it in many searches, but never an actual precise definition. All I know so far is that ...
0answers
58 views

### handle moves: proof

In several 4-manifold textbooks, when handle moves (creation, cancellation, sliding) are discussed, they are explained using very helpful drawings. However, I would like to know if there is a ...
0answers
71 views

### What is the “Standard” Open Book Decomposition for $\mathbb R^n$, and why does this matter?

I am trying to understand better Open book decompositions. To that effect, I tried to work out a couple of (relatively-simple) examples, specifically, for $\mathbb R^2$ and higher. But I have not ...
0answers
356 views

### The Birman–Hilden Theorem and the Nielsen–Thurston classification

So this post is half question/half reference request, as I'm sure it's the kind of thing people would have thought about before (and indeed the question might even be trivial), but I've been unable to ...
0answers
176 views

### Hairy ball theorem: references to applications

I'm looking for references to applications of the Hairy ball theorem. I already visited wikipedia and cited references, but I need a little more explanation in both meteorology and applications in ...
1answer
128 views

### Status of PL topology

I'm starting to learn about geometric topology and manifold theory. I know that there are three big important categories of manifolds: topological, smooth and PL. But I'm seeing that while topological ...
0answers
67 views

### Sufficient conditions for “2-sphericity” of orientable triangulated 2d surface in 3d space

Let $T$ be finite set of tetrahedrons in $\mathbb{R}^3$. Let $T$ be tetrahedral complex in a sense that if two tetrahedrons intersect, the intersection is a face of both. Let $\partial T$ consist of ...
4answers
1k views

### Reference on Geometric Topology

Geometric topology is more motivated by objects it wants to prove theorems about. Geometric topology is very much motivated by low-dimensional phenomena -- and the very notion of low-dimensional ...
1answer
201 views

### Pinched torus generalization

The pinched torus is homeomorphic to a sphere with two (different) points identified.           What is the name and topological structure of the ...
0answers
61 views

### Fundamental Domain of Manifold Reference Request

I am interested in learning about the fundamental domain of a manifold and I am wondering if anyone know of any papers or descriptions online other than Wikipedia and the linked articles? I am looking ...