米尔诺-伍德几何学不平等
Inégalités de Milnor-Wood géométriques
摘要：
本文证明了Milnor-Wood不等式在几何情形下的一个推广。研究了紧致流形的基本群到同维秩一空间乘积的等距群的表示，并给出了表示的体积的一个上界。当目标群为实双曲空间的等距群时，利用Schläfli公式证明了变形下体积的不变性，并对T. Soma;其结果是，由给定的闭三元流形支配的闭双曲三元流形只有1000个。
英文摘要：
We prove an extension of Milnor-Wood inequalities to a geometric situation. We study representations of the fundamental group of a compact manifold into the isometry group of a product of rank one spaces of the same dimension and show an upper bound on the volume of the representation. When the target group is the isometry group of the real hyperbolic space, we show the constance of the volume under deformations using the Schläfli formula and deduce a new and simple proof of a result of T. Soma; the result is that there are only finitely many closed hyperbolic three-manifolds dominated by a given closed three-manifold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
