论文标题
签名，用于在边界上表面上平坦的单一捆绑包
Signature for flat unitary bundles over surfaces with boundary
论文作者
论文摘要
本文介绍了紧凑型表面的基本群体的表示，这些表面具有边界为遗传学类型的经典简单谎言群体。我们将Atiyah-Patodi-Singer相关的本地系统的签名与Burger-iozzi-Wienhard的托莱多不变式联系起来。为了衡量差异，我们将Atiyah-Patodi-singer的Rho不变性扩展为最初定义在$ \ mathrm {u}（p）$上，以不连续的类函数，首先在$ \ mathrm {u}（p，q）上，然后通过嵌入$ \ \ m mathrm {u} $在$ \ mathdings of $ \ mathrm {u} $上。这样，我们以统一的方式提出了三个不同的不变式 - 签名，托莱多和Rho不变式，这是Atiyah-Patodi-Singer的经典签名公式的一种版本，用于具有边界的歧管。
This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems of Atiyah-Patodi-Singer, to Burger-Iozzi-Wienhard's Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer's rho invariant, initially defined on $\mathrm{U}(p)$, to discontinuous class functions, first on $\mathrm{U}(p,q)$, and then on other classical groups via embeddings into $\mathrm{U}(p,q)$. In this way, we present three different invariants -- signature, Toledo and rho invariant -- in a unifying way, which is a version of the classical signature formula of Atiyah-Patodi-Singer for manifolds with boundary.
