A generalized <i>π</i><sub>2</sub>-diffeomorphism finiteness theorem

doi:10.1007/s11464-020-0834-0

Front. Math. China

2020, Vol. 15

Issue (2) : 399-418 https://doi.org/10.1007/s11464-020-0834-0

RESEARCH ARTICLE

A generalized π₂-diffeomorphism finiteness theorem

Xiaochun RONG¹, Xuchao YAO²(

)

¹. Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 USA
². School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

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Abstract

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:

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

Corresponding Author(s): Xuchao YAO

Issue Date: 18 May 2020

Cite this article:

Xiaochun RONG,Xuchao YAO. A generalized π₂-diffeomorphism finiteness theorem[J]. Front. Math. China, 2020, 15(2): 399-418.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0834-0
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I2/399

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