A generalized π2-diffeomorphism finiteness theorem

Xiaochun Rong; Xuchao Yao

doi:10.1007/s11464-020-0834-0

A generalized π₂-diffeomorphism finiteness theorem

Xiaochun Rong, Xuchao Yao

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	399-418
Number of pages	20
Journal	Frontiers of Mathematics in China
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s11464-020-0834-0
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

Access to Document

10.1007/s11464-020-0834-0

Cite this

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