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Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the xed point set M G ≠φ and dim M G = 0, then G has a subgroup H with G/H ∼= Z₂, the cyclic groupof order 2. The tangential representation γx (M ) of G at x ∈M G is alsoregarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.
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참고문헌 (5)
참고문헌 신청
D. Y. Suh / 1988 / Isotropy representations of cyclic group actions on homotopy spheres / Bulletin of the Korean Mathematical Society 25 (2) : 175 ~ 178
G. E. Bredon / 1972 / Introduction to Compact Transformation Groups, Pure and Applied Mathematics / Academic Press
K. Kawakubo / 1991 / The Theory of Transformation Groups, Translated from the 1987 Japanese edition. The Clarendon Press / Oxford University Press
P. A. Smith / 1960 / New results and old problems in finite transformation groups / Bulletin of the American Mathematical Society 66 : 401 ~ 415
S. E. Cappell / 1982 / Fixed points of periodic differentiable maps / Inventiones mathematicae 68 (1) : 1 ~ 19
G. E. Bredon / 1972 / Introduction to Compact Transformation Groups, Pure and Applied Mathematics / Academic Press
K. Kawakubo / 1991 / The Theory of Transformation Groups, Translated from the 1987 Japanese edition. The Clarendon Press / Oxford University Press
P. A. Smith / 1960 / New results and old problems in finite transformation groups / Bulletin of the American Mathematical Society 66 : 401 ~ 415
S. E. Cappell / 1982 / Fixed points of periodic differentiable maps / Inventiones mathematicae 68 (1) : 1 ~ 19
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