Abstract
The purpose of this paper is to generalize a theorem of Segal proving that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding space of continuous maps through a range of dimensions increasing with degree. We will address if a similar result holds when other almost-complex structures are put on a projective space. For any compatible almost-complex structure on , we prove that the inclusion map from the space of –holomorphic maps to the space of continuous maps induces a homology surjection through a range of dimensions tending to infinity with degree. The proof involves comparing the scanning map of topological chiral homology with analytic gluing maps for –holomorphic curves . This is an extension of the author’s work regarding genus-zero case.
Citation
Jeremy Miller. "The topology of the space of $J$–holomorphic maps to $\mathbb{C}\mathrm{P}^2$." Geom. Topol. 19 (4) 1829 - 1894, 2015. https://doi.org/10.2140/gt.2015.19.1829
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