Configuration Spaces and the Topology of Curves in Projective Space

2000/03/13 by Sadok Kallel, Kallel, Sadok · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AG #math.AT #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0003010

24pages

arxiv created 2001/06/29 · arxiv updated 2009/11/30

Abstract

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≥ 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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