Geometric realization of 𝜋₀ℰ(ℳ)

Lee, Kyung Bai

doi:10.1090/S0002-9939-1982-0667306-1

Geometric realization of $\pi _0\mathcal {E}(M)$
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Proc. Amer. Math. Soc. 86 (1982), 353-357 Request permission

Abstract:

Let $M$ be a closed flat Riemannian manifold, $\varepsilon (M)$ the group of self homotopy equivalences of $M$. Then there exists a subgroup ${A_1}(M)$ of $\operatorname {Aff} (M)$ such that the natural homomorphism of ${A_1}(M)$ into ${\pi _0}\varepsilon (M)$ is a surjection with kernel a finite abelian group. Furthermore, this kernel can be identified with the structure group of the Calabi fibration.

References

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Realization of homotopy classes

1

Seifert relatives of flat manifolds

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