相关论文: On Subdivision Posets of Cyclic Polytopes
We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
The $g$-vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds…
The self-duality of the paracyclic category is extended to a certain class of homotopy categories of (2,1)-categories. These generalise the orbit category of a group and are associated to certain self-dual preorders equipped with a presheaf…
In the paper of Montgomery, D. and Yang, C.T. [5], they discuss the de-suspension of smooth free actions of S1 on (2n+1)-dimensional homotopy spheres. In this paper we discuss the de-suspension of smooth free actions of S3 on (4n +…
We classify the polycyclic totally ordered simple dimension groups, i.e. dimension groups given by a dense embedding of n-dimensional lattice into the real line. Our method is based on the geometry of simple geodesics on the hyperbolic…
Given a (finite) simplicial complex, we define its $i$-th Laplacian polytope as the convex hull of the columns of its $i$-th Laplacian matrix. This extends Laplacian simplices of finite simple graphs, as introduced by Braun and Meyer. After…
Cyclic polytopes have been studied since at least the early last century by Caratheodory and others.A generalization is a construction of a class of polytopes such that the polytopes have some of their properties.The best known example is…
We study the simplicial volume of manifolds obtained from Davis' reflection group trick, the goal being characterizing those having positive simplicial volume. In particular, we focus on checking whether manifolds in this class with nonzero…
We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…
Let p be an odd prime and let P be a p-group. We examine the order complex of the poset of elementary abelian subgroups of P having order at least p^2. S. Bouc and J. Th\'evenaz showed that this complex has the homotopy type of a wedge of…
Triangulated categories coming from cyclic posets were originally introduced by the authors in [IT15b] as a generalization of the constructions of various triangulated categories with cluster structures. We give an overview, then analyze…
We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, but need to satisfy a certain connectivity…
In the $2$-dimensional $n$-body problem, $n\ge 3$, in spaces of constant curvature, $\kappa\ne 0$, we study polygonal homographic solutions. We first provide necessary and sufficient conditions for the existence of these orbits and then…
In 1995, Josckusch constructed an infinite family of centrally symmetric (cs, for short) triangulations of $3$-spheres that are cs-$2$-neighborly. Recently, Novik and Zheng extended Jockusch's construction: for all $d$ and $n>d$, they…
Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied.…
Linear upper bounds are provided for the size of the torsion homology of negatively curved manifolds of finite volume in all dimensions $d\ne 3$. This extends a classical theorem by Gromov. In dimension $3$, as opposed to the Betti numbers,…
An abstract $n$-polytope $\mathcal{P}$ is a partially-ordered set which captures important properties of a geometric polytope, for any dimension $n$. For even $n \ge 2$, the incidences between elements in the middle two layers of the Hasse…
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…
The dimension of a partially ordered set $P$ (poset for short) is the least positive integer $d$ such that $P$ is isomorphic to a subposet of $\mathbb{R}^d$ with the natural product order. Dimension is arguably the most widely studied…