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Geometric realization of $ \pi_0\mathcal{E}(M)$


Author: Kyung Bai Lee
Journal: Proc. Amer. Math. Soc. 86 (1982), 353-357
MSC: Primary 57S17; Secondary 53C30, 57R50, 57S15, 58D05
DOI: https://doi.org/10.1090/S0002-9939-1982-0667306-1
MathSciNet review: 667306
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0667306-1
Keywords: Geometric realization, flat manifolds, crystallographic groups, homotopy class of self homotopy equivalences, group extensions, affine diffeomorphisms
Article copyright: © Copyright 1982 American Mathematical Society

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