An analogue of the stabilization map for regular Zp actions

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Abstract

Several authors have used the stabilization technique introduced by Boardman to analyze the fixed point structure of a smooth action of a compact Lie group on smooth manifolds. Using regular Zp actions, defined herein, and the bordism groups of regular Zp actions, we show that if there is a regular action of Zp on a smooth manifold and the manifold is not a boundary in the Thom oriented cobordism group mod the ideal of those elements all of whose Pontrjagin numbers are 0 mod p, then the manifold must have some component of its fixed point set of dimension at least half that of the ambient manifold. As a coda to this, we study the relationship between this stabilization map and the factorization of the cyclotomie polynomials over Zp.

Original languageEnglish
Pages (from-to)689-708
Number of pages20
JournalRocky Mountain Journal of Mathematics
Volume24
Issue number2
DOIs
StatePublished - 1994

ASJC Scopus subject areas

  • Mathematics (all)

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