Group actions on spheres with rank one isotropy
نویسندگان
چکیده
منابع مشابه
Group Actions on Spheres with Rank One Prime Power Isotropy
We show that a rank two finite group G admits a finite G-CW-complex X ' S with rank one prime power isotropy if and only if G does not p′-involve Qd(p) for any odd prime p. This follows from a more general theorem which allows us to construct a finite G-CW-complex by gluing together a given G-invariant family of representations defined on the Sylow subgroups of G.
متن کاملGroup Actions on Spheres with Rank One Isotropy
Let G be a rank two finite group, and let H denote the family of all rank one p-subgroups of G, for which rankp(G) = 2. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X ' S with isotropy in H, whose fixed sets are homotopy spheres.
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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.
متن کاملRANK THREE p-GROUP ACTIONS ON PRODUCTS OF SPHERES
Let p be an odd prime. We prove that every rank three p-group acts freely and smoothly on a product of three spheres. To construct this action, we first prove a generalization of a theorem of Lück and Oliver on constructions of G-equivariant vector bundles. We also give some other applications of this generalization.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6567