Concentrated cyclic actions of high periodicity

Authors:
Daniel Berend and Gabriel Katz

Journal:
Trans. Amer. Math. Soc. **323** (1991), 665-689

MSC:
Primary 57S17; Secondary 57R20, 57S15, 58G10

DOI:
https://doi.org/10.1090/S0002-9947-1991-1005074-4

MathSciNet review:
1005074

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Abstract: The class of concentrated periodic diffeomorphisms is introduced. A diffeomorphism is called concentrated if, roughly speaking, its normal eigenvalues range in a small (with respect to the period of and the dimension of ) arc on the circle. In many ways, the cyclic action generated by such a behaves on the one hand as a circle action and on the other hand as a generic prime power order cyclic action. For example, as for circle actions, , provided that the left-hand side is an integer; as for prime power order actions, cannot have a single fixed point if is closed. A variety of integrality results, relating to the usual signatures of certain characteristic submanifolds of the regular neighbourhood of in to via the normal -representations, is established.

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DOI:
https://doi.org/10.1090/S0002-9947-1991-1005074-4

Article copyright:
© Copyright 1991
American Mathematical Society