论文标题
非交通性驳船 - 巨型形态
Non-commutative Barge-Ghys quasimorphisms
论文作者
论文摘要
A（非交通）ULAM准牙作用是从组$γ$到拓扑组$ g $的地图$ q $，因此$ q（xy）q（y）^{ - 1} q（x）^{ - 1} $属于$ g $的固定紧凑型子集。概括了驳船和吉斯的构建，我们在一个封闭的折叠式分段曲率的基本群体上建立了一系列的准畸形，在一个任意的谎言组中取代了价值。这种概括了驳船的准畸形的建筑将准畸形与任何主要的$ g $ unddle与$ m $上的连接相关联。 Kapovich和Fujiwara表明，所有在离散组中采用值的准畸形都可以从群体同构和准肌构造的构建，并在交换组中以值为单位。我们构建驳船类型的准畸形，以$γ$的给定子集上的规定值，对Kapovich和Fujiwara定理产生反示例定理，用于在谎言组中以值为单位。我们的建筑还概述了D. Kazhdan在他的论文``$ε$ - 代表''中证明的结果。 Kazhdan已证明，对于任何$ε> 0 $，存在$ε$ - 代表的基本组，该组的基本组是2属2属，这是由代表性所代表的$ 1/10 $。我们通过构建$ε$的代表来概括他的结果，该组的基本组是负分段曲率的封闭歧管，在任意谎言组中占据值。
A (non-commutative) Ulam quasimorphism is a map $q$ from a group $Γ$ to a topological group $G$ such that $q(xy)q(y)^{-1}q(x)^{-1}$ belongs to a fixed compact subset of $G$. Generalizing the construction of Barge and Ghys, we build a family of quasimorphisms on a fundamental group of a closed manifold $M$ of negative sectional curvature, taking values in an arbitrary Lie group. This construction, which generalizes the Barge-Ghys quasimorphisms, associates a quasimorphism to any principal $G$-bundle with connection on $M$. Kapovich and Fujiwara have shown that all quasimorphisms taking values in a discrete group can be constructed from group homomorphisms and quasimorphisms taking values in a commutative group. We construct Barge-Ghys type quasimorphisms taking prescribed values on a given subset in $Γ$, producing counterexamples to the Kapovich and Fujiwara theorem for quasimorphisms taking values in a Lie group. Our construction also generalizes a result proven by D. Kazhdan in his paper ``On $ε$-representations''. Kazhdan has proved that for any $ε>0$, there exists an $ε$-representation of the fundamental group of a Riemann surface of genus 2 which cannot be $1/10$-approximated by a representation. We generalize his result by constructing an $ε$-representation of the fundamental group of a closed manifold of negative sectional curvature taking values in an arbitrary Lie group.
