由相伴偏序重构拟同构与Polterovich问题
Reconstructing quasimorphisms from associated partial orders and a question of Polterovich
摘要：
我们证明了有限维1-连通单李群上的每一个连续齐次拟同构都是该群上任何连续双不变偏序的相对增长。更一般地，我们表明，一个任意的齐次拟同构可以重建为相对增长的偏序受到一定的三明治条件。这提供了一个不变的顺序和有界上同调之间的联系，并允许具体计算的相对增长有限维单李群以及某些无限维李群所产生的辛几何。
英文摘要：
We show that every continuous homogeneous quasimorphism on a finite-dimensional 1-connected simple Lie group arises as the relative growth of any continuous bi-invariant partial order on that group. More generally we show, that an arbitrary homogeneous quasimorphism can be reconstructed as the relative growth of a partial order subject to a certain sandwich condition. This provides a link between invariant orders and bounded cohomology and allows the concrete computation of relative growth for finite dimensional simple Lie groups as well as certain infinite-dimensional Lie groups arising from symplectic geometry.
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