# Questions tagged [triangulations]

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17 questions
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### Homeomorphisms of the sphere mapping a geodesic triangulation to another one

Consider the standard Riemannian 2-sphere $S$, equipped with a geodesic triangulation $T$. Let $L(S,T)$ be the space of homeomorphisms of $S$ which map $T$ to a geodesic triangulation. What is the ...
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### Does any smooth oriented closed orbifold have a fundamental class

This thread:triangulation of orbifolds has shown that any smooth closed orbifold has a triangulation. My further question is: if the difference of any two triangulations $P$ and $Q$ is a boundary of a ...
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### Existence of triangulation of Lipschitz domains

Consider a bounded Lipschitz domain $\Omega \subset \mathbb R^n$. Q1: Can its closure $\overline\Omega$ be triangulated? Q2: If yes, can the triangulation be chosen as finite? Furthermore, how ...
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### Homotoping a 2-plane field on a closed orientable 3-manifold to a contact structure

I am a beginner in Contact Geometry. To prove that the inclusion $\text{Cont}(M)\hookrightarrow \text{Dist}(M)$ induces surjection at $\pi_0$ level, the closest I got was based on Ko Honda's notes. ...
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### dissections and vertices of non-convex polytopes

Let us call a finite union $P$ of $n$-dimensional compact convex polytopes in $\mathbb{R}^n$ a non-convex polytope. Recall that a dissection of $P$ is a finite collection $T$ of $n$-dimensional ...
In a triangulation $\Gamma$ of a (oriented) 2-manifold, consider a 2-simplex labeled by ($123$), where $1,2,3$ denote the order of vertices. Consider the dual $\Gamma^*$ of $\Gamma$, and then denote ...