Concentrated cyclic actions of high periodicity

Daniel Berend, Gabriel Katz

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)665-689
Number of pages25
JournalTransactions of the American Mathematical Society
Volume323
Issue number2
DOIs
StatePublished - 1 Jan 1991

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