Bundles with periodic maps and mod 𝑝 Chern polynomial

Jaworowski, Jan

doi:10.1090/S0002-9939-03-07168-5

Bundles with periodic maps and mod $p$ Chern polynomial
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Proc. Amer. Math. Soc. 132 (2004), 1223-1228 Request permission

Abstract:

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

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