Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-03-07168-5
Published electronically: August 20, 2003
MathSciNet review: 2045442
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. J. E. Connett, On the cohomology of fixed-point sets and coincidence-point sets,, Indiana Univ. Math. J. 24 (1974-75), 627-634. MR 51:1805
  • 2. A. Dold, Parametrized Borsuk-Ulam theorems, Comm. Math. Helv. 63 (1988), 275-285. MR 89h:55001
  • 3. J. Jaworowski, Fibre preserving involutions and the kernel of the derivative (preprint), Forschungsinstitut fuer Mathematik ETH Zuerich, August, 1980.
  • 4. J. Jaworowski, Fibre preserving maps of sphere bundles into vector space bundles, Lecture Notes in Mathematics 886, Springer-Verlag, New York, 1981, pp. 143-150. MR 83a:55002
  • 5. J. Jaworowski, The Index of Free Circle Actions in Lens Spaces, Topology and its Appl. 123 (2002), 125-129. MR 2003g:57057
  • 6. J. W. Milnor and J. D. Stasheff, Characteristic Classes, Annals of Math. Studies 76, Princeton University Press, Princeton, NJ, 1974. MR 55:13428
  • 7. R. M. Switzer, Algebraic Topology - Homotopy and Homology, Grundlehren der mathematischen Wissenschaften, Band 212, Springer-Verlag, Berlin-Heidelberg-New York, 1975. MR 52:6695

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55R91, 55R40, 55M20

Retrieve articles in all journals with MSC (2000): 55R91, 55R40, 55M20


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-03-07168-5
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

American Mathematical Society