Frontiers of Mathematics in China >
A generalized π2-diffeomorphism finiteness theorem
Received date: 28 Feb 2020
Accepted date: 17 Apr 2020
Published date: 15 Apr 2020
Copyright
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:
Xiaochun RONG , Xuchao YAO . A generalized π2-diffeomorphism finiteness theorem[J]. Frontiers of Mathematics in China, 2020 , 15(2) : 399 -418 . DOI: 10.1007/s11464-020-0834-0
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