A generalized π₂-diffeomorphism finiteness theorem

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

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