Related papers: Multitriangulations on the half-cylinder

A pseudo-triangle is a simple polygon with exactly three convex vertices, and all other vertices (if any) are distributed on three concave chains. A pseudo-triangulation~$\mathcal{T}$ of a point set~$P$ in~$\mathbb{R}^2$ is a partitioning…

We define an invariant, which we call surface-complexity, of compact 3-manifolds by means of Dehn surfaces. The surface-complexity is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting…

Simplicial geometries are collections of simplices making up a manifold together with an assignment of lengths to the edges that define a metric on that manifold. The simplicial analogs of the Einstein equations are the Regge equations.…

We consider the action of the symmetric group $S_n$ on the permutahedron $\Pi_n$. We prove that if $\sigma$ is a permutation of $S_n$ which has $m$ cycles of lengths $l_1, \ldots, l_m$, then the subpolytope of $\Pi_n$ fixed by $\sigma$ has…

For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the converse implication is known to be true for $p$-forms in…

We analyze the indicial roots of the self-dual deformation complex on a cylinder $(\mathbb{R} \times Y^3, dt^2 + g_Y)$, where $Y^3$ is a space of constant curvature. An application is the optimal decay rate of solutions on a self-dual…

The author has already proven that the space $\Delta(\Pi_n)/G$ is homotopy equivalent to a wedge of spheres of dimension $n-3$ for all natural numbers $n\geq 3$ and all subgroups $G\subset S_1\times S_{n-1}$. We construct an $S_1\times…

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is…

The coefficient forms \( {}_{a} \ell_{k} \) and the para-Eisenstein series \(\alpha_{k}\) are simplicial Drinfeld modular forms. We study the attached simplicial complexes \(\mathcal{BT}^{r}( {}_{a} \ell_{k})\) and…

We discuss $\pmb{SC}_*$, a simplicial homotopy model of $K(Z,2)$ constructed from circular permutations. In any dimension, the number of simplices in the model is finite. The complex $\pmb{SC}_*$ naturally manifests as a simplicial set…

In 2017, Ehrenborg, Govindaiah, Park, and Readdy defined the van der Waerden complex ${\tt vdW}(n,k)$ to be the simplicial complex whose facets correspond to all the arithmetic sequences on the set $\{1,\ldots,n\}$ of a fixed length $k$. To…

Acting with non-Abelian T-duality on the $S^3$ inside the $AdS_5$ subspace of $AdS_5\times S^5$ with $N$ units of flux, we generate a new half-BPS solution with $SU(2|4)$ symmetry that belongs to the Lin-Lunin-Maldacena class of geometries.…

We determine the scaling dimension $\Delta_n$ for the class of composite operators $\phi^n$ in the $\lambda \phi^4$ theory in $d=4-\epsilon$ taking the double scaling limit $n\rightarrow \infty$ and $\lambda \rightarrow 0$ with fixed…

We study half-BPS surface operators in N=2 supersymmetric QCD in four dimensions with gauge group SU(2) and four fundamental flavours. We compute the twisted chiral superpotential that describes the effective theory on the surface operator…

For the ordered set $[n]$ of $n$ elements, we consider the class $\Bscr_n$ of bases $B$ of tropical Pl\"ucker functions on $2^{[n]}$ such that $B$ can be obtained by a series of mutations (flips) from the basis formed by the intervals in…

For integers $d \geq 2$ and $\epsilon = 0$ or 1, let $S^{1, d - 1}(\epsilon)$ denote the sphere product $S^{1} \times S^{d - 1}$ if $\epsilon = 0$ and the twisted $S^{d - 1}$ bundle over $S^{1}$ if $\epsilon = 1$. The main results of this…

The symmetric group $S_3$ acts on $S^2 \times S^2 \times S^2$ by coordinate permutation, and the quotient space $(S^2 \times S^2 \times S^2)/S_3$ is homeomorphic to the complex projective space $\CC P^3$. In this paper, we construct an…

We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show that they generate a closed algebra including…

We construct a phase space for a three dimensional cellular complex with decorations on edges and faces using crossed modules (strict 2-groups) equipped with a (non-trivial) Poisson structure. We do not use the most general crossed module,…

This paper provides (in french) a framework for an alternative demonstration of result of Khimshiashvili and Panina on the characterization of critical points of the area on the manifold of polygons with fixed sidelengths as being the…