论文标题
$ sl_n（\ mathbb r）$的COCOCOCOCACT晶格的几何循环和有限的共同体学
Geometric cycles and bounded cohomology for a cocompact lattice in $SL_n(\mathbb R)$
论文作者
论文摘要
我们显示存在以$ sl_n（\ mathbb r）/so（n）$建模的本地对称歧管$ m $，以及$ dim $ dim（m） - lank（m）$的非平凡同源性类别，由完全测量的Submanifold表示，其中包含一个圆圈。结果，比较映射$ c^k：h_b^k（m，\ mathbb r）\ rightArrow h^k（m，\ mathbb r）$在$ k = dim（m）-rank（m）-rank（m）$中不折点。这提供了与Lafont-Wang的结果相对应的，该结果始终在$ k \ geq dim（m）-lank（m）+2 $的程度上汇总。
We show there exists a closed locally symmetric manifold $M$ modeled on $SL_n(\mathbb R)/SO(n)$, and a non-trivial homology class in degree $dim(M)-rank(M)$ represented by a totally geodesic submanifold that contains a circle factor. As a result, the comparison map $c^k:H_b^k(M,\mathbb R)\rightarrow H^k(M,\mathbb R)$ is not surjective in degree $k=dim(M)-rank(M)$. This provides a counterpart to a result of Lafont-Wang which states that $c^k$ is always surjective in degree $k\geq dim(M)-rank(M)+2$.
