On the topology of the evaluation map and rational curves

Details On the topology of the evaluation map and rational curves On the topology of the evaluation map and rational curves

2006-03-10

arxiv.org/abs/math/0603255v3

Internat. J. Math. 19 (2008), no. 4, 369-385.

Mathematics

Symplectic Geometry

improved versions of the results; stylistic corrections; 15 pages

Scientific paper

10.1142/S0129167X0800473X

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).

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