AI 中文总结
该研究计算紧秩一对称空间的Rabinowitz环同调的BV代数结构，证明其弦点可逆性与欧拉特征和系数域特征的关系，推广了Hingston等人的相关结果。
AI 中文摘要
我们计算了紧秩一对称空间的Rabinowitz环同调的Batalin-Vilkovisky（BV）代数结构。作为推论，我们证明这类空间满足称为弦点可逆性的自然同调条件当且仅当它的欧拉特征等于环同调系数域的特征。这意味着Viterbo关于余切圆盘丛中正合拉格朗日子流形谱范数一致有界猜想的某些情形成立。此外，我们证明当紧秩一对称空间是弦点可逆时，其环同调类关于任意黎曼度量的临界水平满足关于次数的共振条件和关于闭测地线的密度条件。这将Hingston和Rademacher针对球面的结果推广到更广泛的紧秩一对称空间类。
英文摘要
We calculate the Batalin-Vilkovisky (BV) algebra structure of Rabinowitz loop homology for compact rank one symmetric spaces. As a consequence, we prove that such a space satisfies a natural homological condition called string point invertibility if and only if its Euler characteristic is equal to the characteristic of the coefficient field for loop homology. This implies certain cases of Viterbo's conjecture on a uniform bound on the spectral norm of exact Lagrangian submanifolds in cotangent disk bundles. Furthermore, we prove that whenever a compact rank one symmetric space is string point invertible, the critical levels of its loop homology classes with respect to an arbitrary Riemannian metric satisfy a resonance condition with respect to degrees and a density condition for closed geodesics. This generalizes results of Hingston and Rademacher for spheres to a broader class of compact rank one symmetric spaces.
Comments68 pages, no figures
