余切丛上的拟态射与辛均匀化
Quasi-morphisms on cotangent bundles and symplectic homogenization
摘要：
对于一类闭流形N，我们构造了余切丛T*N的Hamilton群G上的函数族。这些限制在一个给定的余切球丛的支持下的Hamilton生成的子群上的齐次拟态射。该族由N的第一实上同调参数化，并且在N=T^n的情况下，它与Viterbo的辛均匀化算子一致。这些功能有应用的代数和几何结构的G及其子群，辛刚性，并奥布里-马瑟和弱KAM理论。
英文摘要：
For a class of closed manifolds N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T*N. These restrict to homogeneous quasi-morphisms on the subgroup generated by Hamiltonians with support in a given cotangent ball bundle. The family is parametrized by the first real cohomology of N, and in the case N=T^n, it coincides with Viterbo's symplectic homogenization operator. These functions have applications to the algebraic and geometric structure of G and its subgroups, to symplectic rigidity, and to Aubry-Mather and weak KAM theory.
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