Open Access
June 2001 A Remark on Torsion Euler Classes of Circle Bundles
Shigeaki MIYOSHI
Tokyo J. Math. 24(1): 189-194 (June 2001). DOI: 10.3836/tjm/1255958322


We show that any torsion class $e\in H^2(M;Z)$ of any closed manifold $M$ is realized as the Euler class of a smoothly foliated orientable circle bundle over $M$. In the case where $M$ is a 3-manifold, we construct the homomorphism $\pi_1(M)\rightarrow SO(2)\subset \text{Diff}_{+}^{\infty}(S^{1})$ explicitly whose Euler class is the given torsion class.


Download Citation

Shigeaki MIYOSHI. "A Remark on Torsion Euler Classes of Circle Bundles." Tokyo J. Math. 24 (1) 189 - 194, June 2001.


Published: June 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1011.57008
MathSciNet: MR1844428
Digital Object Identifier: 10.3836/tjm/1255958322

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

Vol.24 • No. 1 • June 2001
Back to Top