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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Free $S^{3}$-actions on $2$-connected nine-manifolds

Author: Richard I. Resch
Journal: Trans. Amer. Math. Soc. 225 (1977), 107-112
MSC: Primary 57E25
MathSciNet review: 0426004
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Abstract: In this paper a classification of free ${S^3}$-actions on 2-connected 9-manifolds is obtained by examining the corresponding principal ${S^3}$-bundles. The orbit spaces that may occur are determined and it is proved that there are exactly two homotopy classes of maps from each of these spaces into the classifying space for principal ${S^3}$-bundles. It is shown that the total spaces of the corresponding bundles are distinct, yielding the main result that for each nonnegative integer k, there exist exactly two 2-connected 9-manifolds which admit free ${S^3}$-actions and, furthermore, the actions on each of these manifolds are unique.

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Keywords: Free <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img4.gif" ALT="${S^3}$">-action, principal <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${S^3}$">-bundle, Puppe sequence
Article copyright: © Copyright 1977 American Mathematical Society