16,400 research outputs found
Topological methods for complex-analytic Brauer groups
Using methods from algebraic topology and group cohomology, I pursue
Grothendieck's question on equality of geometric and cohomological Brauer
groups in the context of complex-analytic spaces. The main result is that
equality holds under suitable assumptions on the fundamental group and the
Pontrjagin dual of the second homotopy group. I apply this to Lie groups, Hopf
manifolds, and complex-analytic surfaces.Comment: 20 pages, minor corrections, to appear in Topolog
The topological K-theory of certain crystallographic groups
Let Gamma be a semidirect product of the form Z^n rtimes Z/p where p is prime
and the Z/p-action on Z^n is free away from the origin. We will compute the
topological K-theory of the real and complex group C*-algebra of Gamma and show
that Gamma satisfies the unstable Gromov-Lawson-Rosenberg Conjecture. On the
way we will analyze the (co-)homology and the topological K-theory of the
classifying spaces BGamma and underbar{B}Gamma. The latter is the quotient of
the induced Z/p-action on the torus T^n.Comment: 46 pages. Final version. Accepted for publication in the Journal of
Noncommutative Geometr
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