All Questions
Tagged with dg.differential-geometry triangulations
7 questions
11
votes
2
answers
326
views
Triangulation with simplices of same volume
Let $M$ be a Riemannian smooth compact manifold.
It is known that $M$ has a triangulation, for any dimension. But do we know if there exists a triangulation such that all simplices have same volume ?
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11
votes
2
answers
2k
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Proving the Gauss-Bonnet theorem for embedded surfaces using triangulations
I heard this really neat elementary proof of the "Gauss-Bonnet Theorem" :
Let $S$ be a surface embedded in $\mathbb{R}^3$. Now take a triangulation of that surface, and approximate the surface with a ...
10
votes
0
answers
742
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Can any smooth triangulation of a smooth manifold be blurred?
For the purposes of this question, let's say that a blurring
of a smooth triangulation $T$ of a smooth manifold $X$
is a smooth homotopy $h\colon [0,1] \times X \to X$ such that $h_0=\operatorname{id}...
- 37.8k
7
votes
1
answer
260
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Bordism for oriented triangulable manifolds without smooth differentiable structures
We know the bordism group for oriented smooth differentiable structures such as $\Omega_d^{SO}$ that requires the special orthogonal group structure on the tangent bundle $TM$ of manifold $M$.
$$\...
- 10.5k
3
votes
1
answer
136
views
Surfaces generated by minimum-weight triangulations
The minimum-weight triangulation of simple polygons can be efficiently calculated in $O(n^3)$ time by dynamic programming, while it is $\text{NP-hard}$ for pointsets in general.
Looking at the ...
- 13.2k
1
vote
1
answer
258
views
A totally geodesic triangulation
Let $M$ be a compact orientable $n$ dimensional Riemannian manifold.
Is there a triangulation of $M$ such that every $k$ dimensional face of each simplex is a totally geodesic submanifold, $\forall k ...
- 366
0
votes
0
answers
125
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Naming convention for different type of triangulations
When studying random geometries and related mathematical/physical stuff conflicting naming convention pops up regarding the naming of the different ensemble types of triangulations (in general ...
- 183