Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry

J. Cheeger, X. Rong

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study the class of n-Riemannian manifolds in the title such that the torsion elements in the fundamental group have a definite bound on their orders. Our main result asserts the existence of a kind of generalized Seifert fiber structure on Mn, for which the fundamental group of fibers injects into that of Mn. This provides a necessary and sufficient topological condition for a manifold to admit a sufficiently collapsed metric in our class. Among other consequences we obtain a strengthened version of the "gap conjecture" in this context.

Original languageEnglish (US)
Pages (from-to)141-163
Number of pages23
JournalGeometric and Functional Analysis
Issue number2
StatePublished - Mar 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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