Symplectic mapping class groups of some Stein and rational surfaces

Details Symplectic mapping class groups of some Stein and rational surfaces Symplectic mapping class groups of some Stein and rational surfaces

2009-09-30

arxiv.org/abs/0909.5622v3

Journal of Symplectic Geometry 2011 9(1):45-82

Mathematics

Symplectic Geometry

31 pages; updated with minor corrections to agree with published version

Scientific paper

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 $\RP{2}$ and of $\CC^*\times\CC$. 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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