Publications de l'Institut Mathématique, Nouvelle Série Vol. 99(113), pp. 43–49 (2016) 

ON KNASTER'S PROBLEMMarija JelicFaculty of Mathematics, University of Belgrade, Belgrade, SerbiaAbstract: 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. Keywords: $G$equivariant mapping; Dold's theorem; cohomological index; Knaster's problem; configuration space; Stiefel manifold Classification (MSC2000): 52A35; 55N91; 05E18; 55M20 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.
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