TY - JOUR

T1 - Concentrated cyclic actions of high periodicity

AU - Berend, Daniel

AU - Katz, Gabriel

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968476311&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1991-1005074-4

DO - 10.1090/S0002-9947-1991-1005074-4

M3 - Article

AN - SCOPUS:84968476311

VL - 323

SP - 665

EP - 689

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -