论文标题
有限的共同形态和杯赛的无限总和有限的同谋
Infinite sums of Brooks quasimorphisms and cup products in bounded cohomology
论文作者
论文摘要
我们研究了自由组的一类准态性，可以表示为带有一些不错特性的Brooks准畸形的无限总和。然后，我们回顾了Heuer在Arxiv：1710.03193中开发的分解框架，并将这些准晶体放在这种情况下。这使我们能够证明具有琐碎的真实系数的自由组的有限共同体中的许多杯子产品。最后，我们引入了免费分解产品，并将它们与Rolli的自由产品的绝对形态相关联。关于这些问题的技术结果，这仍然是一个悬而未决的问题，这意味着杯子产品的实质性很大。
We study a class of quasimorphisms of the free group that can be expressed as infinite sums of Brooks quasimorphisms with some nice properties. We then review Heuer's framework of decompositions developed in arXiv:1710.03193, and put these quasimorphisms in that context. This allows us to prove triviality of a number of cup products in the bounded cohomology of the free group with trivial real coefficients. Finally, we introduce free products of decompositions and relate them to Rolli's quasimorphisms of free products. A technical result concerning these, which remains an open question, implies a strong triviality result for the cup product.
