Calabi quasimorphism and quantum homology
Calabi quasimorphism and quantum homology
复制标题
DOI：
10.1155/s1073792803210011
复制
发表时间：
2002-05
期刊：
影响因子：
--
通讯作者：
Michael Entov;L. Polterovich
中科院分区：
文献类型：
--
作者：
Michael Entov;L. Polterovich
证明了2-球面的保面积拟同态群与真实的数有非平凡的齐次拟同构，并具有下列性质。它在球面的一个足够小的开子集中支持的任何复同态上的值等于复同态的卡拉比不变量。这个结果推广到更一般的辛流形：如果辛流形是单调的，并且它的量子同调代数是半单的，我们在Hamilton同调同态群的泛覆盖上构造了一个类似的拟同构。
We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small open subset of the sphere equals to the Calabi invariant of the diffeomorphism. This result extends to more general symplectic manifolds: If the symplectic manifold is monotone and its quantum homology algebra is semi-simple we construct a similar quasimorphism on the universal cover of the group of Hamiltonian diffeomorphisms.