紧同态与Hermite对称空间
Tight homomorphisms and Hermitian symmetric spaces
摘要：
在具有非零有界上同调的局部紧群中引入了紧同态的概念，并在目标为埃尔米特型李群时详细研究了这些同态。厄米特型李群之间的紧同态产生厄米特对称空间的紧全测地映射。我们表明，紧映射的行为在函子的方式就Shilov边界，并使用这证明了一个一般的结构定理紧同态。此外，我们还对Poincare圆的紧嵌入进行了分类。
英文摘要：
We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetric spaces. We show that tight maps behave in a functorial way with respect to the Shilov boundary and use this to prove a general structure theorem for tight homomorphisms. Furthermore we classify all tight embeddings of the Poincare' disk.
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。
