Symplectic mapping class groups of some Stein and rational surfaces

By Jonathan D. Evans. 2009

59 citations recorded by the source corpus.

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

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de6c55e27796348a79d0b7852b5c2a62bf7f573b

How researchers see this paper

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In Geometry and Topology

1. Weiwei Wu
2. Tian-Jun Li
3. S. Bauer
4. D. Mcduff

In Mathematical Physics

1. Weiwei Wu
2. Tian-Jun Li
3. D. Mcduff

Citations in the corpus

• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group (2010, background): “Evans [16] calculated explicitly the homotopy type of Symph(M,ω) when (M,ω) is a symplectic Del Pezzo surface with χ ≤ 8 (also known to M.”