Algebraic Realization for Cyclic Group Actions
نویسندگان
چکیده
Suppose G is a finite cyclic group and M a closed smooth G–manifold. In this paper we will show that there is a nonsingular real algebraic G–variety X which is equivariantly diffeomorphic to M and all G–vector bundles over X are strongly algebraic.
منابع مشابه
Algebraic Realization for Cyclic Group Actions with One Isotropy Type
Suppose G is a cyclic group and M a closed smooth G– manifold with exactly one isotropy type. We will show that there is a nonsingular real algebraic G–variety X which is equivariantly diffeomorphic to M and all G–vector bundles over X are strongly algebraic.
متن کاملAlgebraic Realization for Cyclic Group Actions with One Isotropy Type
Suppose G is a cyclic group and M a closed smooth G– manifold with exactly one isotropy type. We will show that there is a nonsingular real algebraic G–variety X which is equivariantly diffeomorphic to M and all G–vector bundles over X are strongly algebraic.
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In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminolo...
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Connolly and Geist have reduced the problem of determining which free cyclic actions on spheres extend to free actions of specified supergroups to a problem involving a certain transfer map. In this note we develop some algebraic tools for calculating the transfer and show that some cyclic actions do not extend to certain supergroups.
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تاریخ انتشار 2010