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

Let $\pi: P\to B$ be a locally trivial fiber bundle over a connected CW complex $B$ with fiber equal to the closed symplectic manifold $(M,\om)$. Then $\pi$ is said to be a symplectic fiber bundle if its structural group is the group of…

Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…

In this paper, we study hyperrigidity for $C^*$-algebras. We will show that hyperrigidity can be expressed solely in terms of representations, without the need to involve general unital completely positive maps.

Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric manifolds, in the context of stably complex manifolds with compatible torus action. By way of application, we give an explicit construction of a…

The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…

Unlike the situation in the classical theory of convex polytopes, there is a wealth of semi-regular abstract polytopes, including interesting examples exhibiting some unexpected phenomena. We prove that even an equifacetted semi-regular…

We show that any smooth lattice polytope P with codegree greater or equal than (dim(P)+3)/2 (or equivalently, with degree smaller than dim(P)/2), defines a dual defective projective toric manifold. This implies that P is Q-normal (in the…

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…

We investigate some combinatorial properties of convex polytopes simple in edges. For polytopes whose nonsimple vertices are located sufficiently far one from another, we prove an analog of the Hard Lefschetz theorem. It implies Stanley's…

B. Blackadar recently proved that any full corner $pAp$ in a unital C*-algebra $A$ has K-theoretic stable rank greater than or equal to the stable rank of $A$. (Here $p$ is a projection in $A$, and fullness means that $ApA=A$.) This result…

Let $X$ be a $4$-dimensional toric orbifold. If $H^3(X)$ has a non-trivial odd primary torsion, then we show that $X$ is homotopy equivalent to the wedge of a Moore space and a CW-complex. As a corollary, given two 4-dimensional toric…

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has…

We give a new very concrete description of the C*-envelope of the tensor algebra associated to multivariable dynamical system. In the surjective case, this C*-envelope is described as a crossed product by an endomorphism, and as a groupoid…

A polytrope is a tropical polytope which at the same time is convex in the ordinary sense. A $d$-dimensional polytrope turns out to be a tropical simplex, that is, it is the tropical convex hull of $d+1$ points. This statement is equivalent…

We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…

A polytope $P$ is circumscribed about a convex body $\Phi\subset \mathbb{R}^n$ if $\Phi\subset P$ and each facet of $P$ is contained in a support hyperplane of $\Phi$. We say that a convex body $\Phi\subset \mathbb{R}^n$ is a rotor of a…

We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(ex(K)).

We classify projective toric manifolds whose dual variety is not a hypersurface in the dual projective space. Under the standard dictionary between toric geometry and convex geometry, they correspond to certain convex Delzant integer…

This paper is a continuation of our previous work in which we defined the notion of a polytope complex and its $K$-theory. In this paper we produce formulas for the delooping of a simplicial polytope complex and the cofiber of a morphism of…