环路空间中的相交重数与弦拓扑余积
Intersection Multiplicity in Loop Spaces and the String Topology Coproduct
AI总结：
本文研究弦拓扑余积的计算难题，利用环路空间同调类的相交重数，证明该余积及基点弦拓扑余积在特定类流形上平凡，并讨论了相关推论。
摘要：
弦拓扑余积通常被视为弦拓扑中与Chas-Sullivan积相对应的结构。但在某些方面，弦拓扑余积比Chas-Sullivan积难理解得多。尤其是该余积不具备同伦不变性，计算难度似乎也大很多。本文对弦拓扑余积进行了综述，并利用环路空间中同调类的相交重数概念，证明弦拓扑余积与基点弦拓扑余积在若干类流形上是平凡的。具体而言，我们证明当乘积流形的两个因子都具有零欧拉示性数时，弦拓扑余积为零；还证明带截面的纤维丛的全空间上的基点余积是平凡的。我们也讨论了这些结果的推论。
英文摘要：
The string topology coproduct is often perceived as a counterpart in string topology to the Chas-Sullivan product. However, in certain aspects the string topology coproduct is much harder to understand than the Chas-Sullivan product. In particular the coproduct is not homotopy-invariant and it seems much harder to compute. In this article we give an overview over the string topology coproduct and use the notion of intersection multiplicity of homology classes in loop spaces to show that the string topology coproduct and the based string topology coproduct are trivial for certain classes of manifolds. In particular we show that the string topology coproduct vanishes on product manifolds where both factors have vanishing Euler characteristic and we show that the based coproduct is trivial for total spaces of fiber bundles with sections. We also discuss implications of these results.
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。
