A Remark on Torsion Euler Classes of Circle Bundles

MIYOSHI, Shigeaki

Tokyo J. of Math., Tome 24 (2001) no. 2, p. 189-194 / Harvested from Project Euclid

Résumé

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.

Publié le : 2001-06-15
Classification:

@article{1255958322,
     author = {MIYOSHI, Shigeaki},
     title = {A Remark on Torsion Euler Classes of Circle Bundles},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 189-194},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958322}
}

MIYOSHI, Shigeaki. A Remark on Torsion Euler Classes of Circle Bundles. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  189-194. http://gdmltest.u-ga.fr/item/1255958322/