We develop an equivariant Dixmier-Douady theory for locally trivial bundles of C⁎-algebras with fibre D⊗K equipped a fibrewise T-action, where T denotes the circle group and D=End(V)⊗∞ T-representation V. In particular, we show that T-equivariant ⁎-automorphisms AutT(D⊗K) is infinite loop space giving rise to cohomology ED,T⁎(X). Isomorphism classes then form respect tensor product isomorphic E...

There is lymph humor/lymphocytopoietic factor (LHF) in various tissues. However, a definite substance or a definite combination of any substances of LHF in thoracic duct lymph remains unknown. Justification for the conception of a new approach to revealing of LHF composition in native thoracic duct lymph is based on a discovery of mitoses in native thoracic duct lymph of normal immature rabbits...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand, principal 2-group [G → Aut(G)]bundles over Lie groupoids (i.e. [G → Aut(G)]-bundles over differentiable stacks) and, on the other hand, centralG-extensions of Lie groupoids (i.e. Ggerbes over differentiable stacks). We also introduce universal characteristic classes for 2-group bundle...

Using the methods of the noncommutative geometry and the K–theory, we prove that the well–known Dixmier–Douady invariant of continuous–trace C –algebras and the Godbillon– Vey invariant of the codimension–1 foliations on compact manifolds coincide in a class of the so–called ”foliation derived” C–algebra bundles. Moreover, with the help of such bundles both of the above invariants admit an eleg...

We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is di erent from the original one, given by Douady and Hubbard and re ned by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depende...