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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bundles with periodic maps and mod $p$ Chern polynomial


Author: Jan Jaworowski
Journal: Proc. Amer. Math. Soc. 132 (2004), 1223-1228
MSC (2000): Primary 55R91, 55R40; Secondary 55M20
Published electronically: August 20, 2003
MathSciNet review: 2045442
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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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Additional Information

Jan Jaworowski
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405-5701
Email: jaworows@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07168-5
PII: S 0002-9939(03)07168-5
Keywords: Periodic map, fibre preserving map, complex structure, Chern classes, lens space, Chern polynomial, coincidence set
Received by editor(s): August 7, 2002
Received by editor(s) in revised form: November 22, 2002
Published electronically: August 20, 2003
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society