16,400 research outputs found

    Topological methods for complex-analytic Brauer groups

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    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

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    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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