Positive scalar curvature due to the cokernel of the classifying map (Part 1)

I will present a paper jointly written with Thomas Schick, which contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance. Let M be a closed spin manifold of dimension greater or equal to 5 which admits a metric with positive scalar curvature. We give lower bounds on the rank of the group of psc metrics over M up to bordism in terms of the corank of the canonical map KO_*(M) to KO_*(BG), provided the rational analytic Novikov conjecture is true for G, the fundamental group of G.

Since it is a long talk I’ll take the time of introducing basic objects and techniques for those who are not familiar with the subject.