Bundles with periodic maps and mod 𝑝 Chern polynomial

Abstract

Suppose that E → B E\to B is a vector bundle with a linear periodic map of period p p ; the map is assumed free on the outside of the 0 0 -section. A polynomial c E ( y ) c_{E}(y) , called a mod p p Chern polynomial of E E , is defined. It is analogous to the Stiefel-Whitney polynomial defined by Dold for real vector bundles with the antipodal involution. The mod p p Chern polynomial can be used to measure the size of the periodic coincidence set for fibre preserving maps of the unit sphere bundle of E E into another vector bundle.