Related papers: Example of C-rigid polytopes which are not B-rigid

A discrete group with word-length (G,L) is B-isocohomological for a bounding classes B if the comparison map from B-bounded cohomology to ordinary cohomology (with complex coefficients) is an isomorphism; it is strongly B-isocohomological…

A good contact toric manifold $M$ is determined by its moment cone $C$. We compute the equivariant cohomology ring with $\Z$ coefficient of $M$ in terms of the combinatorial data of $C$. Then under a smoothness criterion on the cone $C$, we…

Our main result states that a finite semiring of order >2 with zero which is not a ring is congruence-simple if and only if it is isomorphic to a `dense' subsemiring of the endomorphism semiring of a finite idempotent commutative monoid. We…

Given a reduced crystallographic root system with a fixed simple system, it is associated to a Weyl group $W$, parabolic subgroups $W_K$'s and a polytope $P$ which is the convex hull of a dominant weight. The quotient $P/W_K$ can be…

We give two new constructions of the harmonic algebra of a lattice polytope $P$, a bigraded algebra whose character is the $q$-Ehrhart series of $P$ defined by Reiner and Rhoades. First, we show that the harmonic algebra is the associated…

We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P. We devise a combinatorial method…

Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions…

The Ehrhart ring of the edge polytope $\mathcal{P}_G$ for a connected simple graph $G$ is known to coincide with the edge ring of the same graph if $G$ satisfies the odd cycle condition. This paper gives for a graph which does not satisfy…

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial…

Abstract polytopes generalize the face lattice of convex polytopes. A polytope is semiregular if its facets are regular and its automorphism group acts transitively on its vertices. In this paper we construct semiregular, facet-transitive…

Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…

Given a pure, full-dimensional, locally strongly connected polyhedral complex C with convex support, we characterize, by a local codimension-2 condition, polyhedral complexes that coarsen C. The proof of the characterization draws upon a…

Let $\mathcal{P}$ be a chiral polytope with type $\{k_1, k_2\}$ and $G=Aut(\mathcal{P})$. Suppose $|G|=2p^m$, where $k_1, k_2\geq 3$ and $p$ is an odd prime. Let $P$ be a Sylow $p$-subgroup of $G$. We prove that $G \cong P \rtimes…

A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…

We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes…

String C-groups are precisely the automorphism groups of abstract regular polytopes. A certain regular d-polytope C_d with an automorphism group of order 2^{2d-1}, discovered by Conder and shown to have the smallest number of flags among…

A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…

Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…

We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated…

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a…