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Type: Journal article
Title: Affine simplices in Oka manifolds
Author: Larusson, F.
Citation: Documenta Mathematica, 2009; 14(1):691-697
Publisher: Deutsche Mathematiker Vereinigung
Issue Date: 2009
ISSN: 1431-0643
Statement of
Finnur Lárusson
Abstract: 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.
Keywords: Complex manifold
Stein manifold
Oka manifold
Oka property
simplicial set
singular set
affine simplex
homotopy type
weak equivalence.
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Mathematical Sciences publications

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