Advanced Studies in Pure Mathematics

Pontrjagin classes and higher torsion of sphere bundles

Kiyoshi Igusa

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Abstract

By a classical result of Schafer and Kahn ([12], [6]), oriented topological sphere bundles have well defined rational Pontrjagin classes. In the smooth case, we show that the corresponding Pontrjagin character is proportional to the higher Franz-Reidemeister torsion invariant in each degree when the fiber is even dimensional and we discuss the relationship in the odd dimensional case.

Article information

Source
Groups of Diffeomorphisms: In honor of Shigeyuki Morita on the occasion of his 60th birthday, R. Penner, D. Kotschick, T. Tsuboi, N. Kawazumi, T. Kitano and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2008), 21-29

Dates
Received: 30 April 2007
Revised: 28 December 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447476

Digital Object Identifier
doi:10.2969/aspm/05210021

Mathematical Reviews number (MathSciNet)
MR2509703

Zentralblatt MATH identifier
1231.57025

Citation

Igusa, Kiyoshi. Pontrjagin classes and higher torsion of sphere bundles. Groups of Diffeomorphisms: In honor of Shigeyuki Morita on the occasion of his 60th birthday, 21--29, Mathematical Society of Japan, Tokyo, Japan, 2008. doi:10.2969/aspm/05210021. https://projecteuclid.org/euclid.aspm/1543447476


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