The space of metrics of positive scalar curvature
Abstract
We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements of infinite order in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics. Along the way we construct smooth fiber bundles over spheres whose total spaces have nonvanishing Ahatgenera, thus establishing the nonmultiplicativity of the Ahatgenus in fibre bundles with simply connected base.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.0068
 Bibcode:
 2012arXiv1212.0068H
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Topology;
 Mathematics  Differential Geometry
 EPrint:
 24 pages, v2: minor additions and corrections, based in particular on comments of referees, v3: minor corrections, final version, to appear in Publ.Math. IHES