2015/07/08 by Frol Zapolsky, Zapolsky, Frol · 4 citations
Mathematics · Medicine · #53D12 (secondary) #53D40 (primary) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1507.02253
openalex publication_date 2015/07/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The purpose of this paper is to extend the construction of the PSS-type\nisomorphism between the Floer homology and the quantum homology of a monotone\nLagrangian submanifold L of a symplectic manifold M, provided that the\nminimal Maslov number of L is at least two, to arbitrary coefficients. We\nprovide a proof, again over arbitrary coefficients, that this isomorphism\nrespects the natural algebraic structures on both sides, such as the quantum\nproduct and the quantum module action. This isomorphism serves as the technical\nfoundation for the construction of Lagrangian spectral invariants in a joint\npaper with Remi Leclercq (arXiv:1505:07430). Our constructions work when the\nsecond Stiefel--Whitney class of L vanishes on the image of the boundary\nhomomorphism \π3(M,L) \→ \π2(L), a condition strictly weaker than being\nrelatively Pin; in particular we do not require L to be orientable. The\nconstructions are done using canonical orientations, and require no further\nchoices such as relative Pin-structures. Such structures do however play a\nsignificant role when endowing the various complexes and homologies with\nstructures of modules over Novikov rings, and in calculations.\n