involutions on the nonorientable
-sphere bundle over
Author:
Paik Kee Kim
Journal:
Proc. Amer. Math. Soc. 55 (1976), 449-452
DOI:
https://doi.org/10.1090/S0002-9939-1976-0394717-1
MathSciNet review:
0394717
Full-text PDF Free Access
Abstract | References | Additional Information
Abstract: We show that there are exactly nine distinct involutions on the nonorientable
-sphere bundle over
, up to
equivalences. This, together with results of [1], [3] and [8], classifies all
involutions on the
-sphere bundles over
.
- [1]
R. L. Fremon, Finite cyclic group actions on
, Thesis, Michigan State University, East Lansing, Mich., 1969.
- [2]
P. K. Kim and J. L. Tollefson, Splitting the
involutions on nonprime
-manifolds (to appear).
- [3] Kyung Whan Kwun, Piecewise linear involutions of 𝑆¹×𝑆², Michigan Math. J. 16 (1969), 93–96. MR 242161
- [4] G. R. Livesay, Fixed point free involutions on the 3-sphere, Ann. of Math. (2) 72 (1960), 603–611. MR 116343, https://doi.org/10.2307/1970232
- [5] G. R. Livesay, Involutions with two fixed points on the three-sphere, Ann. of Math. (2) 78 (1963), 582–593. MR 155323, https://doi.org/10.2307/1970543
- [6] P. A. Smith, Transformations of finite period. II, Ann. of Math. (2) 40 (1939), 690–711. MR 177, https://doi.org/10.2307/1968950
- [7] Jeffrey L. Tollefson, Free involutions on non-prime 3-manifolds, Osaka Math. J. 7 (1970), 161–164. MR 266184
- [8] Jeffrey L. Tollefson, Involutions on 𝑆¹×𝑆² and other 3-manifolds, Trans. Amer. Math. Soc. 183 (1973), 139–152. MR 326738, https://doi.org/10.1090/S0002-9947-1973-0326738-0
- [9] Friedhelm Waldhausen, Über Involutionen der 3-Sphäre, Topology 8 (1969), 81–91 (German). MR 236916, https://doi.org/10.1016/0040-9383(69)90033-0
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1976-0394717-1
Keywords:
-sphere bundles over
,
involution,
fixed-point set
Article copyright:
© Copyright 1976
American Mathematical Society