Correction for the paper “S 3 -bundles and exotic actions”
Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 4, pp. 543-545.

In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7-spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7-spheres that occur as quotients of the free S 3 -actions described above.

On construit dans [R] des représentants explicites des fibrés principaux de fibre S 3 au-dessus de S 7  ; on en déduit des actions libres et explicites de S 3 , dont les quotients sont des sphères exotiques de dimension 7. La description de ces actions est basée sur une formule de classification des fibrés. Or cette formule est incorrecte. Le théorème 1 corrige cette formule ainsi que la formule de classification ; le théorème 2 exhibe les indices corrects des sphères exotiques de dimension 7 qui apparaissent comme quotient des actions libres de S 3 .

DOI: 10.24033/bsmf.2407
Classification: 57R22, 55R25, 57R60
Keywords: principal bundles, exotic spheres, exotic actions
Mot clés : fibrés principaux, sphères exotiques, actions exotiques
@article{BSMF_2001__129_4_543_0,
     author = {Barros, T. E.},
     title = {Correction for the paper {\textquotedblleft}$S^3$-bundles and exotic actions{\textquotedblright}},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {543--545},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {129},
     number = {4},
     year = {2001},
     doi = {10.24033/bsmf.2407},
     mrnumber = {1894149},
     zbl = {0993.57015},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2407/}
}
TY  - JOUR
AU  - Barros, T. E.
TI  - Correction for the paper “$S^3$-bundles and exotic actions”
JO  - Bulletin de la Société Mathématique de France
PY  - 2001
SP  - 543
EP  - 545
VL  - 129
IS  - 4
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.2407/
DO  - 10.24033/bsmf.2407
LA  - en
ID  - BSMF_2001__129_4_543_0
ER  - 
%0 Journal Article
%A Barros, T. E.
%T Correction for the paper “$S^3$-bundles and exotic actions”
%J Bulletin de la Société Mathématique de France
%D 2001
%P 543-545
%V 129
%N 4
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/bsmf.2407/
%R 10.24033/bsmf.2407
%G en
%F BSMF_2001__129_4_543_0
Barros, T. E. Correction for the paper “$S^3$-bundles and exotic actions”. Bulletin de la Société Mathématique de France, Volume 129 (2001) no. 4, pp. 543-545. doi : 10.24033/bsmf.2407. http://www.numdam.org/articles/10.24033/bsmf.2407/

[1] T. Barros & A. Rigas - « The role of commutators in a non-cancellation phenomenon », Math. J. Okayama Univ. (to appear). | MR | Zbl

[2] K. Grove & W. Ziller - « Curvature and symmetry of the Milnor spheres », Ann. of Math. (2) 152 (2000), no. 1, p. 331-367. | MR | Zbl

[3] S. Hu - Homotopy theory, Academic Press, 1959. | MR | Zbl

[4] A. Rigas - « S 3 -bundles and exoctic actions », Bull. Soc. Math. France 112 (1984), p. 69-92. | Numdam | MR | Zbl

Cited by Sources: