Mathematics – K-Theory and Homology
Scientific paper
2010-07-02
Mathematics
K-Theory and Homology
32 pages. Changes in v3: minor referee-suggested revisions. Changes in v2: changed title; improved computational results in th
Scientific paper
Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G (minus 2), in the sense that T. Lawson's Bott map is an isomorphism on homotopy in these dimensions. We establish a periodicity theorem for crystallographic subgroups of the isometries of k-dimensional Euclidean space. For a certain subclass of torsion-free crystallographic groups, we prove a vanishing result for the homotopy groups of the stable moduli space of representations, and we provide examples relating these homotopy groups to the cohomology of G. These results are established as corollaries of the fact that for each n > 0, the one-point compactification of the moduli space of irreducible n-dimensional representations of G is a CW complex of dimension at most k. This is proven using real algebraic geometry and projective representation theory.
No associations
LandOfFree
Periodicity in the stable representation theory of crystallographic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Periodicity in the stable representation theory of crystallographic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodicity in the stable representation theory of crystallographic groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-727570