On configuration spaces of stable maps

Details On configuration spaces of stable maps On configuration spaces of stable maps

2011-04-28

arxiv.org/abs/1104.5440v2

Mathematics

Symplectic Geometry

Fixed a problem with bibliography

Scientific paper

We study here some aspects of the topology of the space of smooth stable genus 0 maps (of a Riemann surface) into a Riemannian manifold $X$, i.e. the Kontsevich stable maps which are not necessarily holomorphic. We use the Hofer-Wysocki-Zehnder polyfold structure on this space and some natural characteristic classes to show that for $X=BU$ the rational homology of the spherical mapping space injects into the rational homology of the space of stable maps. We also give here a definition of what we call $q$-complete symplectic manifolds, which roughly speaking means Gromov-Witten theory captures all information about homology of the space of smooth stable maps.

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