Geodesic
On Knaster's Problem
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 43 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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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     author = {Marija Jeli\'c},
     title = {On {Knaster's} {Problem}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {43 },
     year = {2016},
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     number = {113},
     doi = {10.2298/PIM151030032J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM151030032J/}
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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

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