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Homotopy type of space of maps into a ▫$K(G,n)$▫Smrekar, JakaNaj 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.Source: Homology, homotopy, and applications. - ISSN 1532-0073 (Vol. 15, no. 1, 2013, str. 137-149)Type of material - article, component partPublish date - 2013Language - englishCOBISS.SI-ID - 16643929
Author
Smrekar, Jaka
Topics
matematika |
topologija |
funkcijski prostor |
homotopski tip |
Eilenberg-Mac Laneov prostor |
Abelov momoid |
mathematics |
topology |
function space |
homotopy type |
Eilenberg-Mac Lane space |
abelian monoid
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Smrekar, Jaka | 21969 |
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