AI 中文总结
研究流形、配边和同调类的莫尔斯复杂度，通过手术理论证上界、指标理论证下界，得出允许离散序列表示的李群的局部对称空间莫尔斯复杂度随体积线性增长，且不允许开书分解的结论。
AI 中文摘要
流形的莫尔斯复杂度是构建它所需的最少柄数。我们探索流形、配边和同调类的莫尔斯复杂度，利用手术理论证明非平凡上界，利用指标理论证明下界。我们最复杂的结果表明，对于允许离散序列表示的李群，其局部对称空间的莫尔斯复杂度随体积线性增长。这意味着这样的局部对称空间不允许开书分解。
英文摘要
The Morse complexity of a manifold is the minimal number of handles required to build it. We explore the Morse complexity of manifolds, bordisms, and homology classes, proving nontrivial upper bounds using surgery theory and lower bounds using index theory. Our most involved result shows that for Lie groups which admit discrete series representations, the Morse complexity of their locally symmetric spaces grows linearly with volume. This implies that such locally symmetric spaces do not admit open book decompositions.
CommentsFormerly an appendix to arXiv:2311.16389, which will be edited to remove the appendix once this article is posted
