Torus actions on cohomological complex projective spaces

Wang, Kai

doi:10.1090/S0002-9939-1977-0461543-5

Torus actions on cohomological complex projective spaces
HTML articles powered by AMS MathViewer

by Kai Wang PDF

Proc. Amer. Math. Soc. 65 (1977), 355-356 Request permission

Abstract:

In this note, we will compute the Pontrjagin classes of those topological manifolds which have the same rational cohomology algebra as $C{P^n}$ and which admit effective topological ${T^n}$ actions.

References

F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
Wu-yi Hsiang, Cohomology theory of topological transformation groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 85, Springer-Verlag, New York-Heidelberg, 1975. MR 0423384
Ted Petrie, Torus actions on homotopy complex projective spaces, Invent. Math. 20 (1973), 139–146. MR 322893, DOI 10.1007/BF01404062
James A. Schafer, Topological Pontrjagin classes, Comment. Math. Helv. 45 (1970), 315–332. MR 275443, DOI 10.1007/BF02567335
Kai Wang, Decomposability of homotopy lens spaces and free cyclic group actions on homotopy spheres, Trans. Amer. Math. Soc. 220 (1976), 361–371. MR 431237, DOI 10.1090/S0002-9947-1976-0431237-4