Non-negative pinching, moduli spaces and bundles with infinitely many souls

Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We show that in each dimension n ≤ 10, there exist infinite sequences of homotopy equivalent, but mutually non-homeomorphic closed simply connected Riemannian n-manifolds with 0 ≥ sec ≥ 1, positive Ricci curvature and uniformly bounded diameter. We also construct open manifolds of fixed diffeomorphism type which admit infinitely many complete non-negatively pinched metrics with souls of bounded diameter such that the souls are mutu- ally non-homeomorphic. Finally, we construct examples of non-compact manifolds whose moduli spaces of complete metrics with sec ≤ 0 have infinitely many connected components.

Original languageEnglish (US)
Pages (from-to)365-383
Number of pages19
JournalJournal of Differential Geometry
Volume71
Issue number3
DOIs
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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