23.05.2013
Dr. Malte Röer
14:00 Uhr
Abstract. Let π be a finite group. There is a geometric description of KO_{*}(B π) which represents classes by compact spin manifolds. Taking the p-invariants of Dirac operators associated with these spin manifolds gives a homomorphism KO_{*}(B π) → A, where A is a suitable abelian group. The ρ-invariant in this form has been used to prove special cases of the Gromov-Lawson-Rosenberg conjecture.
On the other hand, there is Greenlees' algebraic approach to KO-homology which describes KO_{*}(B π) in terms of local cohomology groups of modules over the representation ring RO(π).
In our talks we explain how to relate the geometric construction of the ρ-invariant to the algebraic picture by constructing a homomorphism
ρ ̂_{*} : Ω_{*} ^{Spin} (Bπ) → H^{1}_{JO(π)} (KO_{π}^{-* -1})
taking values in the _rst local cohomology group of Atiyah-Segal π –equivariant KO-theory. We show that the invariant ρ ̂ is equivalent to ρ.
Raum 1C-04
im Allianzgebäude (05.20)