On the topology of the evaluation map and rational curves
Symplectic Geometry
2008-04-22 v3 Geometric Topology
Abstract
We explore a relationship between topological properties of orbits of 2-cycles in the symplectomorphism group Symp(M) and the existence of rational curves in M. Under the absence of rational curves hypothesis, we show that evaluation map vanishies on the second homotopy group and obtain a Gottlieb-type vanishing theorem for toroidal cycles in Symp(M).
Keywords
Cite
@article{arxiv.math/0603255,
title = {On the topology of the evaluation map and rational curves},
author = {Gerasim Kokarev},
journal= {arXiv preprint arXiv:math/0603255},
year = {2008}
}
Comments
improved versions of the results; stylistic corrections; 15 pages