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Maps into \(\mathbb{R} P^ 2\) and applications. (English) Zbl 0852.55024
Bureš, J. (ed.) et al., The proceedings of the Winter school Geometry and topology, Srní, Czechoslovakia, January 1992. Palermo: Circolo Matemático di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 32, 155-163 (1994).
Let \(V\) be a closed surface and \(P^2\) be the projective plane. The set \([V,P^2]\) of all homotopy classes of maps has some interesting connections with relativistic kinks of Lorentz’s metric tensor of relativity theory. Earlier J. G. Williams and the author had completely determined the structure of the set \([V,P^2]\) in [Kink metrics in \((2+1)\)-dimensional space-time, J. Math. Phys. 33, 256-266 (1992)]. However, those results are based on earlier works of J. F. Adams [Bull. Lond. Math. Soc. 14, 533-534 (1982; Zbl 0517.58007)] and P. Olum [Trans. Am. Math. Soc. 103, 30-44 (1962; Zbl 0135.23203)].
In this note the author has provided a detailed but precise description of “Orientation True” and “Compressible” maps from \(V\) to \(P^2\) along with several illustrative examples. This further clarifies the structure of the set \([V,P^2]\) with regard to the above concepts.
For the entire collection see [Zbl 0794.00022].
Reviewer: S.Deo (Jabalpur)
55S37 Classification of mappings in algebraic topology