Related papers: Coxeter groups of stellar manifolds

Holomorphic vector bundles on $\mathbb C\times M$, $M$ a complex manifold, with meromorphic connections with poles of Poincar\'e rank 1 along $\{0\}\times M$ arise naturally in algebraic geometry. They are called $(TE)$-structures here.…

In this paper we survey $n$-dimensional solenoidal manifolds for $n=1,2$ and 3, and present new results about them. Solenoidal manifolds of dimension $n$ are metric spaces locally modeled on the product of a Cantor set and an open…

In this article, we introduce rotation groups as a common generalisation of Coxeter groups and graph products of groups (including right-angled Artin groups). We characterise algebraically these groups by presentations (periagroups) and we…

The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the…

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general…

We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and canonically defined $k$-stacked ball. In…

Using geometric arguments, we compute the group of homotopy classes of maps from a closed $(n+1)$-dimensional manifold to the $n$-sphere for $n \geq 3$. Our work extends results from Kirby, Melvin and Teichner for closed oriented…

Poincar\'e profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this paper we calculate the Poincar\'e profiles of all connected…

Nestohedra are a family of convex polytopes that includes permutohedra, associahedra, and graph associahedra. In this paper, we study an extension of such polytopes, called extended nestohedra. We show that these objects are indeed the…

We derive presentations of the interval groups related to all quasi-Coxeter elements in the Coxeter group of type $D_n$. Type $D_n$ is the only infinite family of finite Coxeter groups that admits proper quasi-Coxeter elements. The…

We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic…

For arbitrary integer n, we describe a large class of right-angled Coxeter systems for which the visual baundary (of the corresponding Coxeter-Davis complex) is homeomorphic to the n-dimensional Sierpi\'nski compactum. We also provide a…

The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…

We show that bi-flat $F$-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter…

We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs $(X,\epsilon R)$ over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of…

A covariant Poisson bracket and an associated covariant star product in the sense of deformation quantization are defined on the algebra of tensor-valued differential forms on a symplectic manifold, as a generalization of similar structures…

We give complete geometric invariants of cobordisms of framed fold maps. These invariants consist of two types. We take the immersion of the fold singular set into the target manifold together with information about non-triviality of the…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds,…

The authors give a short survey of previous results on $\delta$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal…

This paper is an introductory and informal exposition on the topology of polygonal meshes. We begin with a broad overview of topological notions and discuss how homeomorphisms, homotopy, and homology can be used to characterise topology. We…