论文标题
在较高等级的对称空间的字符串拓扑上
On the string topology of symmetric spaces of higher rank
论文作者
论文摘要
可以通过明确的周期研究紧凑的全球对称空间的自由环和基于的环路空间的同源性。我们使用Bott和Samelson和Ziller构建的周期来研究紧凑型对称空间上的弦拓扑结构和Chas-Sullivan产品。我们表明，紧凑型对称空间的Chas-Sullivan产品对于任何等级来说都是高度不平凡的，我们证明有许多非努力类，其功能与封闭的大地测量学的迭代相对应。此外，我们表明，基于较高等级的紧凑型对称空间的基于基于的弦拓扑构造是微不足道的，并且我们研究了该结果对弦拓扑的含义对自由环空间的含义。
The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the Chas-Sullivan product on compact symmetric spaces. We show that the Chas-Sullivan product for compact symmetric spaces is highly non-trivial for any rank and we prove that there are many non-nilpotent classes whose powers correspond to the iteration of closed geodesics. Moreover, we show that the based string topology coproduct is trivial for compact symmetric spaces of higher rank and we study the implications of this result for the string topology coproduct on the free loop space.
