Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

Given an affine algebraic variety V and a quantization Oq(V ) of its coordinate ring, it is conjectured that the primitive ideal space of Oq(V ) can be expressed as a topological quotient of V . Evidence in favor of this conjecture is discussed, and positive solutions for several types of varieties (obtained in joint work with E. S. Letzter) are described. In particular, explicit topological qu...

We announce the definition of the dual group, GB(^, of the Fourier-Stieltjes algebra, B(G), of a locally compact group G; and we state four main theorems culminating in the result that GB(G) is a locally compact topological group which is topological^ isomorphic to G. This result establishes an explicit dual relationship between a group and its Fourier-Stieltjes algebra. Moreover, this result e...

I work in an area at the intersection of representation theory, low-dimensional topology, higher category theory, and operator algebras which is often referred to as quantum algebra or quantum topology. A practical description of this field is that it consists of the mathematics which is descended from the Jones polynomial [Jon85]. The unifying idea behind quantum topology is to consider a func...

Classical topological relation expressions and computations are primarily based on abstract algebra. In this article, the representation and computation of geometry-oriented topological relations (GOTR) are developed. GOTR is the integration of geometry and topology. The geometries are represented by blades, which contain both algebraic expressions and construction structures of the geometries ...