ON KNASTER'S PROBLEM

Marija Jelic

Abstract: 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

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