Affine simplices in Oka manifolds
Date
2009
Authors
Larusson, F.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Documenta Mathematica, 2009; 14(1):691-697
Statement of Responsibility
Finnur Lárusson
Conference Name
DOI
Abstract
<jats:p>
We show that the homotopy type of a complex manifold
<jats:inline-formula>
<jats:tex-math>X</jats:tex-math>
</jats:inline-formula>
satisfying the Oka property is captured by holomorphic maps from the affine spaces
<jats:inline-formula>
<jats:tex-math>\mathbb C^n, n\geq 0</jats:tex-math>
</jats:inline-formula>
, into
<jats:inline-formula>
<jats:tex-math>X</jats:tex-math>
</jats:inline-formula>
. Among such
<jats:inline-formula>
<jats:tex-math>X</jats:tex-math>
</jats:inline-formula>
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
<jats:inline-formula>
<jats:tex-math>X</jats:tex-math>
</jats:inline-formula>
is given by a simplicial set whose simplices are holomorphic maps into
<jats:inline-formula>
<jats:tex-math>X</jats:tex-math>
</jats:inline-formula>
.
</jats:p>