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(Mg), 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 Mg 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