# Symplectic mapping class groups of some Stein and rational surfaces - Mathematics > Symplectic Geometry

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Abstract: In this paper we compute the homotopy groups of the symplectomorphism groupsof the 3-, 4- and 5-point blow-ups of the projective plane considered asmonotone symplectic Del Pezzo surfaces. Along the way, we need to compute thehomotopy groups of the compactly supported symplectomorphism groups of thecotangent bundle of $\mathbf{RP}^{2}$ and of $\mathbf{C}^*\times\mathbf{C}$. Wealso make progress in the case of the $A n$-Milnor fibres: here we can showthat the compactly supported Hamiltonian group is contractible and that thesymplectic mapping class group embeds in the braid group on $n$-strands.

Autor: Jonathan David Evans

Fuente: https://arxiv.org/