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Transactions of the American Mathematical Society

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Degree of symmetry of a homotopy real projective space


Authors: H. T. Ku, L. N. Mann, J. L. Sicks and J. C. Su
Journal: Trans. Amer. Math. Soc. 161 (1971), 51-61
MSC: Primary 57.47
DOI: https://doi.org/10.1090/S0002-9947-1971-0282377-X
MathSciNet review: 0282377
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Abstract: The degree of symmetry $ N(M)$ of a compact connected differentiable manifold M is the maximum of the dimensions of the compact Lie groups which can act differentiably and effectively on it. It is well known that $ N(M) \leqq \dim \; SO(m + 1)$, for an m-dimensional manifold, and that equality holds only for the standard m-sphere and the standard real projective m-space. W. Y. Hsiang has shown that for a high dimensional exotic m-sphere M, $ N(M) < {m^2}/8 + 1 < \left( {\frac{1}{4}} \right)\dim SO(m + 1)$, and that $ N(M) = {m^2}/8 + 7/8$ for some exotic m-spheres. It is shown here that the same results are true for exotic real projective spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0282377-X
Keywords: Differentiable manifold, compact Lie group, degree of symmetry, exotic sphere, exotic real projective space
Article copyright: © Copyright 1971 American Mathematical Society

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