Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On spaces of maps between complex projective spaces

Author: Jesper Michael Møller
Journal: Proc. Amer. Math. Soc. 91 (1984), 471-476
MSC: Primary 55P15; Secondary 58D15
MathSciNet review: 744651
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: When $ 1 \leqslant m \leqslant n$, the space $ M({P^m},{P^n})$ of maps of complex projective $ m$-space $ {P^m}$ into complex projective $ n$-space $ {P^n}$ has a countably infinite number of components enumerated by degrees of maps in $ {H^2}({P^m};{\mathbf{Z}})$. By calculating their $ (2n - 2m + 1)$-dimensional integral homology group we show that two components of $ M({P^m},{P^n})$ are homotopy equivalent if and only if their associated degrees have the same absolute value.

References [Enhancements On Off] (What's this?)

  • [1] V. L. Hansen, The homotopy problem for the components in the space of maps on the $ n$-sphere, Quart. J. Math. Oxford Ser. (3) 25 (1974), 313-321. MR 0362396 (50:14838)
  • [2] -, On the space of maps of a closed surface into the $ 2$-sphere, Math. Scand. 35 (1974), 149-158. MR 0385919 (52:6778)
  • [3] -, On spaces of maps of $ n$-manifolds into the $ n$-sphere, Trans. Amer. Math. Soc. 265 (1981), 273-281. MR 607120 (82c:55014)
  • [4] S. T. Hu, Concerning the homotopy groups of the components of the mapping space $ {Y^S}$, Indag. Math. 8 (1946), 623-629.
  • [5] S. Sasao, The homotopy of $ {\operatorname{Map}}(C{P^m},C{P^n})$, J. London Math. Soc. (2) 8 (1974), 193-197. MR 0346783 (49:11507)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P15, 58D15

Retrieve articles in all journals with MSC: 55P15, 58D15

Additional Information

Keywords: Homotopy classification of components of mapping spaces, restriction fibration, primary obstruction, Gysin sequence
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society