On Geroch’s counterexample to the algebraic Hopf conjecture

Klembeck, Paul F.

doi:10.1090/S0002-9939-1976-0428225-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Geroch’s counterexample to the algebraic Hopf conjecture
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by Paul F. Klembeck PDF

Proc. Amer. Math. Soc. 59 (1976), 334-336 Request permission

Abstract:

In this paper we present a simplified version of Geroch’s counterexample to the algebraic Hopf conjecture which requires only a knowledge of the formal symmetries of Riemannian curvature tensors.

References

R. L. Bishop and S. I. Goldberg, Some implications of the generalized Gauss-Bonnet theorem, Trans. Amer. Math. Soc. 112 (1964), 508–535. MR 163271, DOI 10.1090/S0002-9947-1964-0163271-8
Robert Geroch, Positive sectional curvatures does not imply positive Gauss-Bonnet integrand, Proc. Amer. Math. Soc. 54 (1976), 267–270. MR 390961, DOI 10.1090/S0002-9939-1976-0390961-8

Algebraic curvatures and curvatures