Journal article

Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds

  • Dessai, Anand Département de Mathématiques, Université de Fribourg, Swizerland
  • Klaus, Stephan Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach-Walke, Germany
  • Tuschmann, Wilderich Karlsruher Institut für Technologie, Fakultät für Mathematik, Karlsruhe, Germany
Published in:
  • Bulletin of the London Mathematical Society. - 2018, vol. 50, no. 1, p. 96-107
English We show that in each dimension $4n+3$, $n\ge 1$, there exist infinite sequences of closed smooth simply connected manifolds $M$ of pairwise distinct homotopy type for which the moduli space of Riemannian metrics with nonnegative sectional curvature has infinitely many path components. Closed manifolds with these properties were known before only in dimension seven, and our result does also hold for moduli spaces of Riemannian metrics with positive Ricci curvature. Moreover, in conjunction with work of Belegradek, Kwasik and Schultz, we obtain that for each such $M$ the moduli space of complete nonnegative sectional curvature metrics on the open simply connected manifold $M\times\mathbb {R}$ also has infinitely many components.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
License undefined
Persistent URL

Document views: 28 File downloads:
  • des_nms.pdf: 57