Configuration Spaces and the Topology of Curves in Projective Space

Details Configuration Spaces and the Topology of Curves in Projective Space Configuration Spaces and the Topology of Curves in Projective Space

2000-03-13

arxiv.org/abs/math-ph/0003010v2

Physics

Mathematical Physics

24pages

Scientific paper

We survey and expand on the work of Segal, Milgram and the author on the topology of spaces of maps of positive genus curves into $n$-th complex projective space, $n\geq 1$ (in both the holomorphic and continuous categories). Both based and unbased maps are studied and in particular we compute the fundamental groups of the spaces in question. The relevant case when $n=1$ is given by a non-trivial extension which we fully determine.

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