## Abstract

The π_{2}-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 π_{2}-diffeomorphism finiteness by removing the condition that π_{1}(M) = 0 and asserting the diffeomorphism finiteness on the Riemannian universal cover of M.

Original language | English (US) |
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Pages (from-to) | 399-418 |

Number of pages | 20 |

Journal | Frontiers of Mathematics in China |

Volume | 15 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2020 |

## All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

## Keywords

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

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