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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A commutative diagram and an application to differentiable transformation groups

Author: W. D. Curtis
Journal: Proc. Amer. Math. Soc. 31 (1972), 260-264
MathSciNet review: 0290389
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Abstract: A commutative diagram is presented which relates the groups of concordance classes of diffeomorphisms $ \Gamma ({S^{2n}}),\Gamma (C{P^n})$ and $ \Gamma ({S^{2n + 1}})$. This diagram is applied to show that every equivariant diffeomorphism of $ {S^7}$ is concordant to the identity. It follows that the exotic $ 8$-sphere, $ {\Sigma ^8}$, admits no smooth semifree $ {S^1}$-action with exactly two fixed points.

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Keywords: Homotopy sphere, stable $ 1$-stem, Munkres-Milnor pairing, semifree circle group action, concordance, $ J$-homomorphism
Article copyright: © Copyright 1972 American Mathematical Society