On the topology of the evaluation map and rational curves
Abstract
Description
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).
improved versions of the results; stylistic corrections; 15 pages
improved versions of the results; stylistic corrections; 15 pages