Extending free cyclic actions on spheres

Ewing, John

doi:10.1090/S0002-9947-1982-0667168-7

Extending free cyclic actions on spheres

Author: John Ewing
Journal: Trans. Amer. Math. Soc. 273 (1982), 695-703
MSC: Primary 57S17; Secondary 57Q10, 57S25
DOI: https://doi.org/10.1090/S0002-9947-1982-0667168-7
MathSciNet review: 667168
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Connolly and Geist have reduced the problem of determining which free cyclic actions on spheres extend to free actions of specified supergroups to a problem involving a certain transfer map. In this note we develop some algebraic tools for calculating the transfer and show that some cyclic actions do not extend to certain supergroups.

[1] Frank Connolly and Robert Geist, On extending free group actions on spheres and a conjecture of Iwasawa, Trans. Amer. Math. Soc. 274 (1982), no. 2, 631–640. MR 675071, https://doi.org/10.1090/S0002-9947-1982-0675071-1
[2] Kenkichi Iwasawa, On the theory of cyclotomic fields, Ann. of Math. (2) 70 (1959), 530–561. MR 124320, https://doi.org/10.2307/1970328
[3] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358–426. MR 196736, https://doi.org/10.1090/S0002-9904-1966-11484-2
[4] Jean-Pierre Serre, Corps locaux, Hermann, Paris, 1968 (French). Deuxième édition; Publications de l’Université de Nancago, No. VIII. MR 0354618
[5] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. MR 0431216