Symplectic mapping class groups of some Stein and rational surfaces

2009/09/30 by Jonathan David Evans · 1 citation
Mathematics · #math.SG #math.DG #msc:53D35

paper · pdf

published as Journal of Symplectic Geometry 2011 9(1):45-82 · 31 pages; now agrees with published version

arxiv created 2014/05/10 · arxiv updated 2014/05/13

Abstract

In this paper we compute the homotopy groups of the symplectomorphism groups of the 3-, 4- and 5-point blow-ups of the projective plane (considered as monotone symplectic Del Pezzo surfaces). Along the way, we need to compute the homotopy groups of the compactly supported symplectomorphism groups of the cotangent bundle of RP² and of C^*\timesC. We also make progress in the case of the A_n-Milnor fibres: here we can show that the (compactly supported) Hamiltonian group is contractible and that the symplectic mapping class group embeds in the braid group on n-strands.

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