Symplectic mapping class groups of some Stein and rational surfaces
Symplectic mapping class groups of some Stein and rational surfaces
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一些斯坦因曲面和有理曲面的辛映射类群
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发表时间：
2009
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通讯作者：
J. Evans
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文献类型：
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作者：
J. Evans
本文计算了射影平面(被认为是单调Del Pezzo曲面)的3点、4点和5点爆破的辛同构群的同伦群。在此过程中，我们需要计算$mathbf{rp}^{2}$和$mathbf{C}^*imesmathbf{C}$的余切丛的紧支撑辛同构群的同伦群。我们还在$A_n$-Milnor纤维的情况下取得了进展：在这里我们可以证明(紧支撑的)哈密尔顿群是可压缩的，并且辛映射类群嵌入到$n$-链上的辫子群中。
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 $mathbf{C}^* imesmathbf{C}$. 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.