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http://dx.doi.org/10.4134/JKMS.j200249

HOMOTOPY PROPERTIES OF map(ΣnℂP2, Sm)  

Lee, Jin-ho (Data Science, Pulse9. Inc.)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.3, 2021 , pp. 761-790 More about this Journal
Abstract
For given spaces X and Y, let map(X, Y) and map*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map*(X, Y ; g) be the path component of map(X, Y) containing f and map*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane πn+m(ΣnℂP2) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣnℂP2, Sm) up to homotopy equivalence. We also determine the generalized Gottlieb groups Gn(ℂP2, Sm). Finally, we compute homotopy groups of mapping spaces map(ΣnℂP2, Sm; f) for all generators [f] of [ΣnℂP2, Sm], and Gottlieb groups of mapping components containing constant map map(ΣnℂP2, Sm; *).
Keywords
Composition methods; homotopy groups of mapping spaces; cohomotopy groups; Gottlieb groups; evaluation fibrations;
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