余切丛上的部分拟态和拟态以及辛均匀化
Partial quasi-morphisms and quasi-states on cotangent bundles, and symplectic homogenization
摘要：
对于闭连通流形N，我们构造了余切丛T^*N的Hamilton群G上的函数族和T^*N上紧支集的光滑函数空间上的函数族.这些满足类似于Entov和Polterovich的部分准态和准态的性质。族的参数化由N的第一实上同调。在N=T^n的情形下，G上的函数族与维泰博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，奥布里-马瑟理论，限制泊松括号，辛刚性。
英文摘要：
For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on the space of smooth functions with compact support on T^*N. These satisfy properties analogous to those of partial quasi-morphisms and quasi-states of Entov and Polterovich. The families are parametrized by the first real cohomology of N. In the case N=T^n the family of functions on G coincides with Viterbo's symplectic homogenization operator. These functions have applications to the algebraic and geometric structure of G, to Aubry-Mather theory, to restrictions on Poisson brackets, and to symplectic rigidity.
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