Lagrangian Floer-quantum-PSS包与Floer理论中的正则取向
The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
摘要：
本文将辛流形$M$的单调拉格朗日子流形$L$的弗洛尔同调与量子同调之间的PSS型同构的构造推广到任意系数，只要$L$的最小Maslov数至少为2.我们提供了一个证明，再次在任意系数，这种同构尊重双方的自然代数结构，如量子产品和量子模块的行动。这种同构在与Remi Leclercq（arXiv：1505：07430）的联合论文中作为拉格朗日谱不变量的构造的技术基础。我们的建设工作时，第二Stiefel-惠特尼类$L$消失的图像上的边缘同态$π_3(M,L) \to π_2(L)$，一个条件严格弱于相对Pin，特别是我们不需要$L$定向。构造是使用规范方向完成的，并且不需要进一步的选择，例如相对Pin结构。然而，当赋予各种复合物和同调以诺维科夫环上的模的结构时，以及在计算中，这样的结构确实起着重要的作用。
英文摘要：
The purpose of this paper is to extend the construction of the PSS-type isomorphism between the Floer homology and the quantum homology of a monotone Lagrangian submanifold $L$ of a symplectic manifold $M$, provided that the minimal Maslov number of $L$ is at least two, to arbitrary coefficients. We provide a proof, again over arbitrary coefficients, that this isomorphism respects the natural algebraic structures on both sides, such as the quantum product and the quantum module action. This isomorphism serves as the technical foundation for the construction of Lagrangian spectral invariants in a joint paper with Remi Leclercq (arXiv:1505:07430). Our constructions work when the second Stiefel--Whitney class of $L$ vanishes on the image of the boundary homomorphism $π_3(M,L) \to π_2(L)$, a condition strictly weaker than being relatively Pin; in particular we do not require $L$ to be orientable. The constructions are done using canonical orientations, and require no further choices such as relative Pin-structures. Such structures do however play a significant role when endowing the various complexes and homologies with structures of modules over Novikov rings, and in calculations.
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。
