Questions tagged [triangulation]

Question 1

I am writing because in our first course on differential geometry in Spain, our professor has decided to use the concept of triangulation to define integrals of n-forms on differential manifolds, but ...

Question 2

Given an unknown point $P \in \mathbb{R}^2$, you can find its location if you have three known points $A$, $B$, and $C$ and distances $d(A,P) = a$, $d(B,P) = b$, and $d(C,P) = c$. If you're finding an ...

Question 3

This an exercise from Munkres' Algebraic Topology. Are figures 3.9 and 3.10 both triangualtions of $RP^2$, or is 3.10 different? (If yes, then it is deceptively simple). Is it so that only the ...

Question 4

Consider a triangular region (2-cell). The boundary triangle (1-cell) is a boundary because it bounds the 2-cell in the sense that there exists a neighborhood that which belong to the 2-cell and ...

Question 5

One possible approach to defining the surface area of a smooth 2D surface embedded into 3D Euclidean space, which is a natural generalization of the idea of calculating the arc length of a 1D curve as ...

Question 6

Theorem 1.7 in "Curves on 2-manifolds and isotopies" by Epstein says that "If a simple closed curve $S$ on a surface $M$ is homotopic to zero, then it bounds a disk". At one point ...

Question 7

This question is probably known for any expert in geometric topology: Is it true that any two triangulations of the $d$-dimensional ball have a common refinement? As I've learned, this question is ...

Question 8

Is there some material on what are the N-Dimensional Bistellar Flips (Regarding Delaunay Triangulation)? At most I've found this material with the 4D Bistellar Flips: https://arxiv.org/pdf/2312....

Question 9

I'm looking at the simple, locally $C_6$ graphs (open neighbourhood of each vertex is $C_6$) with 16 vertices whose clique complex is a triangulation of a 2-torus (and not a Klein bottle). There are 4 ...

Question 10

I understand that every smooth manifold has a triangulation (into a simplicial complex). I understand that from every triangulation we can define the underlying graph (using the 1-skeleton). Is it a ...

Question 11

I'm trying to derive the recurrence relation for the Catalan numbers using polygon triangulation, but the final result is off by 1 index and I can't find my mistake. Context for the proof can be seen ...

Question 12

Given any set of $3$D points, can we always make non-overlapping tetrahedrons from them where the union of tetrahedrons exactly fill the convex hull of the input points? AFAIK, given any set of $2$D ...

Question 13

For my Topology I class, I had the following exercise: Find a triangulation of $\mathbb{RP}^2$ and draw it. Then, set up the chain complex $C_\bullet(K)$ and compute its homology groups. I should ...

Question 14

I am studying Topology, and recently I learned that every closed surface (2 dimensional manifold) can be triangulated. I understood triangulation as making polygons (with triangles) homeomorphic to ...

Question 15

Suppose $X$ is a CW complex (I use definition in Munkres, Elements of Algebraic Topology), $h:|K|\to X$ is a triangulation, i.e. $|K|$ is simplicial complex and $h$ homeomorphism. Supposed in addition ...

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Questions tagged [triangulation]

References for triangulation of manifolds [closed]

Is it possible to do trilateration with unspecified distance units?

Triangulation of $RP^2$

Simplicial homology does not always count holes?

Does requiring that the triangles in a surface triangulation become small avoid the Schwartz lantern problem?

Triangulation of a manifold with curve as a subcomplex

Hauptvermutung for a ball

N Dimensional Bistellar Flips

Graph invariant that differentiates torus triangulations with different Dehn twist

Is this definition of 'biggest' simplicial complex from a graph well-posed?

Proof that number of polygon triangulations equals the catalan numbers.

Given any set of $3$D points, can we always tetrahedronize them?

The simplicial homology of the real projective plane $\mathbb{RP}^2$

Minimum Number of Triangles for Triangulation of Closed Surfaces

Triangulation of CW Complex Induces Triangulation of Closed Cells

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