Geodesic
Affine simplices in Oka manifolds
Documenta mathematica, Tome 14 (2009), pp. 691-697

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We show that the homotopy type of a complex manifold X satisfying the Oka property is captured by holomorphic maps from the affine spaces Cn,n≥0, into X. Among such X are all complex Lie groups and their homogeneous spaces. We present generalisations of this result, one of which states that the homotopy type of the space of continuous maps from any smooth manifold to X is given by a simplicial set whose simplices are holomorphic maps into X.
DOI : 10.4171/dm/286
Classification : 32C18, 32Q55, 55U10
Mots-clés : complex manifold, Stein manifold, Oka manifold, Oka property, simplicial set, singular set, affine simplex, homotopy type, weak equivalence 
Finnur Lárusson. Affine simplices in Oka manifolds. Documenta mathematica, Tome 14 (2009), pp. 691-697. doi: 10.4171/dm/286
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     author = {Finnur L\'arusson},
     title = {Affine simplices in {Oka} manifolds},
     journal = {Documenta mathematica},
     pages = {691--697},
     year = {2009},
     volume = {14},
     doi = {10.4171/dm/286},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/286/}
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