Obstructions to approximating maps of 2-polyhedra into ▫$\mathbb R^4$▫ by embeddings
Ahmetʹev, Petr Mihajlovič, 1963- ; Repovš, Dušan, 1954-
Dokažemo kriterij za aproksimalnost preslikave ▫$i\circ f$▫ z vložitvami, kjer sta ▫$f:K\to \mathbb R^3$▫ preslikava v splošni legi in ▫$i:\mathbb R^3 \to \mathbb R^4$▫ inkluzija. Kriterij je ...sestavljen iz dveh pogojev. Prvi velja splošneje, za preslikave ▫$K^n \stackrel{f}{\longrightarrow} \mathbb R^{2n-1} \stackrel{i}{\subset} \mathbb R^{2n}$▫. Za ▫$n\ge 3$▫ je prvi pogoj potreben in zadosten, za ▫$n=2$▫ pa je le potreben. Če je ▫$n=2$▫ in je prva ovira nič, vpeljemo drugo. Dokažemo tudi, da je v primeru, ko je ▫$K^2$▫ orientabilna sklenjena ploskev, druga ovira enaka (modulo 2) produktu Arf invariant določenim kvadratnih form.
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