Geodesic
On Knaster's Problem
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 43 .

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Dold's theorem gives sufficient conditions for proving that there is no $G$-equivariant mapping between two spaces. We prove a generalization of Dold's theorem, which requires triviality of homology with some coefficients, up to dimension $n$, instead of $n$-connectedness. Then we apply it to a special case of Knaster's famous problem, and obtain a new proof of a result of C.\,T. Yang, which is much shorter and simpler than previous proofs. Also, we obtain a positive answer to some other cases of Knaster's problem, and improve a result of V.\,V. Makeev, by weakening the conditions.
DOI : 10.2298/PIM151030032J
Classification : 52A35 55N91, 05E18, 55M20
Keywords: $G$-equivariant mapping, Dold's theorem, cohomological index, Knaster's problem, configuration space, Stiefel manifold 
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     title = {On {Knaster's} {Problem}},
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Marija Jelić. On Knaster's Problem. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 43 . doi : 10.2298/PIM151030032J. http://geodesic.mathdoc.fr/articles/10.2298/PIM151030032J/

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