Abstract
Abstract
In this paper we show that the space of holomorphic immersions from any given open Riemann surface
into the Riemann sphere
is weakly homotopy equivalent to the space of continuous maps from
to the complement of the zero section in the tangent bundle of
. It follows in particular that this space has
path components, where
is the number of generators of the first homology group
. We also prove a parametric version of the Mergelyan approximation theorem for maps from Riemann surfaces to an arbitrary complex manifold, a result used in the proof of our main theorem.
Funder
Slovenian Research Agency
Cited by
1 articles.
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