2012/12/31 by Bernhard Hanke, Thomas Schick, Wolfgang Steimle · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #math.GT
paper · pdf · doi:10.1007/s10240-014-0062-9
published as Publ. Math. Inst. Hautes Etudes Sci. 120 (2014), 335-367 · 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
arxiv created 2014/02/12 · openalex publication_date 2014/02/28 · arxiv updated 2015/07/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
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 non-vanishing A-hat-genera, thus establishing the non-multiplicativity of the A-hat-genus in fibre bundles with simply connected base.