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Proceedings of the American Mathematical Society
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744651-4
PII: S 0002-9939(1984)0744651-4
Keywords: Homotopy classification of components of mapping spaces, restriction fibration, primary obstruction, Gysin sequence
Article copyright: © Copyright 1984 American Mathematical Society