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Homotopy type of space of maps into a ▫$K(G,n)$▫
Smrekar, Jaka
Naj bo ▫$X$▫ povezan CW kompleks in naj ▫$K(G,n)$▫, za Abelovo grupo ▫$G$▫, označuje Eilenberg-Mac Laneov CW kompleks. Ker za ▫$K(G,n)$▫ lahko vzamemo Abelov monoid, je šibki homotopski tip prostora ...zveznih preslikav ▫$X \to K(G,n)$▫ odvisen le od homoloških grup kompleksa ▫$X$▫. Namen tega prispevka je dokazati, da enako drži za pravi homotopski tip. Natančneje, dokažemo, da je prostor ▫$\mathrm{map}_\ast\big(X, K(G,n)\big)$▫ zveznih preslikav ▫$X \to K(G,n)$▫, ki spoštujejo bazni točki, homotopsko ekvivalenten kartezičnemu produktu ▫$$\prod_{i \leq n}\mathrm{map}_\ast \big(M_i, K(G,n)\big).$$▫ Tu je ▫$M_i$▫ Moorov CW kompleks tipa ▫$M\big(H_i(X), i\big)$▫. Prostori preslikav so opremljeni s kompaktno odprto topologijo.
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