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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Fixed sets of framed $ G$-manifolds


Author: Stefan Waner
Journal: Trans. Amer. Math. Soc. 298 (1986), 421-429
MSC: Primary 57R85; Secondary 57S17
DOI: https://doi.org/10.1090/S0002-9947-1986-0857451-8
MathSciNet review: 857451
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Abstract: This note describes restrictions on the framed bordism class of a framed manifold $ Y$ in order that it be the fixed set of some framed $ G$-manifold $ M$ with $ G$ a finite group. These results follow from a recently proved generalization of the Segal conjecture, and imply, in particular, that if $ M$ is a framed $ G$-manifold of sufficiently high dimension, and if $ G$ is a $ p$-group, then the number of ``noncancelling'' fixed points is either zero or approaches infinity as the dimension of $ M$ goes to infinity. Conversely, we give sufficient conditions on the framed bordism class of a manifold $ Y$ that it be the fixed set of some framed $ G$-manifold $ M$ of arbitrarily high dimension.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0857451-8
Article copyright: © Copyright 1986 American Mathematical Society

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