## Abstract

The class of concentrated periodic diffeomorphisms g: M → M is introduced. Adiffeomorphism is called concentrated if, roughly speaking, its normal eigenvalues range in a small(with respect to the period of g and the dimension of M) arc on the circle. In many ways, the cyclic action generated by such a g behaveson 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, Sign(g, M) = Sign(M^{g}), provided that the left-hand side is an integer; as for prime power order actions, g cannot have asingle fixed point if M is closed. A variety of integrality results, relating to the usual signatures of certain characteristic submanifolds of the regularneighbourhood of M^{g} in M to Sign(g, M) via thenormal g-representations, is established.

Original language | English |
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Pages (from-to) | 665-689 |

Number of pages | 25 |

Journal | Transactions of the American Mathematical Society |

Volume | 323 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 1991 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics