Bubble Divergences from Twisted Cohomology

Bubble divergences from cellular cohomology

Cohomology of Twisted Tensor Products

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this is still true. We give an explicit description of the Ext-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential part of the Hochschild cohomology ring of a t...

Twisted Jets, Motivic Measure and Orbifold Cohomology

We introduce the notion of twisted jets. For a DeligneMumford stack X of finite type over C, a twisted ∞-jet on X is a representable morphism D → X such that D is a smooth DeligneMumford stack with the coarse moduli space SpecC[[t]]. We study the motivic measure on the space of the twisted ∞-jets on a smooth Deligne-Mumford stack. As an application, we prove that two birational minimal models w...

Twisted Cyclic Cohomology and Modular Fredholm Modules

Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515–526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podleś spheres and from SUq(2).

Twisted K-Theory as a BRST Cohomology

We use the BRST formalism to classify the gauge orbits of type II string theory’s Ramond-Ramond (RR) field strengths under large RR gauge transformations of the RR gauge potentials. We find that this construction is identical to the AtiyahHirzebruch spectral sequence construction of twisted K-theory, where the AtiyahHirzebruch differentials are the BRST operators. The actions of the large gauge...