3
votes
1answer
126 views

Triangulations of a disk, flip distance and hamiltonian circuit

Let us consider a disk with one labelled point on the boundary and $n$ labelled points in the interior. Let T be a triangulation of the whole disk with vertices on the labelled points such that T ...
4
votes
0answers
168 views

Mean number of $n$-simplices per $(n-2)$-simplex in a triangulated $n$-manifold

Work by Tamura (extending results by Luo and Stong) shows the following. Theorem: For any closed 3-manifold $M$ and any rational number $4.5 < r < 6$ there is a triangulation $T$ of $M$ for ...
1
vote
0answers
141 views

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 ...
23
votes
1answer
895 views

High Dimensional Analogs of Polygon Spaces

[Edit: I had a mistake in the numerology (took d=6,5 instead d=5,4). Edit: I mistakingly identified my mistake, it is 6,5 but I got the indices shifted by one.] Background: Polygon spaces Given a ...