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Zbl 0852.55024
Zvengrowski, Peter
Maps into $\bbfR P\sp 2$ and applications. (English)
[A] 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 {\it 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 {\it J. F. Adams} [Bull. Lond. Math. Soc. 14, 533-534 (1982; Zbl 0517.58007)] and {\it P. Olum} [Trans. Am. Math. Soc. 103, 30-44 (1962; Zbl 0135.23203)].\par 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.
[S.Deo (Jabalpur)]

MSC 2000:: *55S37 Classification of mappings

Keywords: Stiefel-Whitney class; compressible maps; Steenrod squares; homotopy classes of maps; Lorentz's metric tensor; relativity theory

Citations: Zbl 0825.53024; Zbl 0517.58007; Zbl 0135.23203

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