A generalized π2-diffeomorphism finiteness theorem

Xiaochun Rong, Xuchao Yao

Research output: Contribution to journalArticlepeer-review


The π2-diffeomorphism finiteness result of F. Fang-X. Rong and A. Petrunin-W. Tuschmann (independently) asserts that the diffeomorphic types of compact n-manifolds M with vanishing first and second homotopy groups can be bounded above in terms of n, and upper bounds on the absolute value of sectional curvature and diameter of M. In this paper, we will generalize this π2-diffeomorphism finiteness by removing the condition that π1(M) = 0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.

Original languageEnglish (US)
Pages (from-to)399-418
Number of pages20
JournalFrontiers of Mathematics in China
Issue number2
StatePublished - Apr 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


  • Collapsing with bounded sectional curvature
  • diffeomorphism finiteness
  • vanishing second homotopy group


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