On spaces of maps between complex projective spaces
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- by Jesper Michael MΓΈller PDF
- Proc. Amer. Math. Soc. 91 (1984), 471-476 Request permission
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
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 471-476
- MSC: Primary 55P15; Secondary 58D15
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744651-4
- MathSciNet review: 744651