On Cohomotopy cocycle spaces (i.e. spaces of maps into an n-sphere):
Vagn Lundsgaard 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 (DOI:10.1093/qmath/25.1.313)
Vagn Lundsgaard Hansen, On Spaces of Maps of $n$-Manifolds Into the $n$-Sphere, Transactions of the American Mathematical Society
Vol. 265, No. 1 (May, 1981), pp. 273-281 (jstor:1998494)
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