Free -actions on simply connected eight-manifolds

Author:
Richard I. Resch

Journal:
Proc. Amer. Math. Soc. **49** (1975), 461-468

MSC:
Primary 57E25; Secondary 55F25

MathSciNet review:
0370633

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Abstract: In this paper the canonical equivalence between free actions of a compact Lie group and principal -bundles is used to apply the theory of fiber bundles to the problem of classifying free differentiable -actions. The orbit spaces that may occur are determined and a calculation of homotopy classes of maps from these spaces into the classifying space for principal -bundles is made with the aid of the Postnikov system for . The bundles corresponding to these classes of maps are then studied to prove that for each positive integer there exist exactly three simply connected -manifolds which admit free differentiable -actions and have second homology group free of rank , and that the action on each of these manifolds is unique. It is also proved that even if the second homology group of the -manifold has torsion, it can admit at most one action.

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0370633-5

Keywords:
Free -action,
principal -bundle,
spin manifold,
Postnikov system,
second Stiefel-Whitney class,
Sq

Article copyright:
© Copyright 1975
American Mathematical Society