Ring Structure of the Floer Cohomology of Σ× S
نویسنده
چکیده
We give a presentation for the Floer cohomology ring HF ∗(Σ × S), where Σ is a Riemann surface of genus g ≥ 1, which coincides with the conjectural presentation for the quantum cohomology ring of the moduli space of flat SO(3)connections of odd degree over Σ. We study the spectrum of the action of H∗(Σ) on HF ∗(Σ× S) and prove a physical assumption made in [1].
منابع مشابه
Fukaya - Floer Homology
We determine the Fukaya-Floer (co)homology groups of the threemanifold Y = Σ × S, where Σ is a Riemann surface of genus g ≥ 1. These are of two kinds. For the 1-cycle S ⊂ Y , we compute the Fukaya-Floer cohomology HFF ∗(Y, S) and its ring structure, which is a sort of deformation of the Floer cohomology HF ∗(Y ). On the other hand, for 1-cycles δ ⊂ Σ ⊂ Y , we determine the Fukaya-Floer cohomolo...
متن کاملThe Z–graded symplectic Floer cohomology of monotone Lagrangian sub–manifolds
We define an integer graded symplectic Floer cohomology and a Fintushel–Stern type spectral sequence which are new invariants for monotone Lagrangian sub–manifolds and exact isotopes. The Z–graded symplectic Floer cohomology is an integral lifting of the usual ZΣ(L) –graded Floer–Oh cohomology. We prove the Künneth formula for the spectral sequence and an ring structure on it. The ring structur...
متن کاملFukaya-floer Homology of Σ × S 1 and Applications
We determine the Fukaya-Floer (co)homology groups of the three-manifold Y = Σ×S, where Σ is a Riemann surface of genus g ≥ 1. These are of two kinds. For the 1-cycle S ⊂ Y , we compute the Fukaya-Floer cohomology HFF ∗(Y, S) and its ring structure, which is a sort of deformation of the Floer cohomology HF (Y ). On the other hand, for 1-cycles δ ⊂ Σ ⊂ Y , we determine the Fukaya-Floer homology H...
متن کاملar X iv : d g - ga / 9 50 10 02 v 3 2 5 Ja n 19 95 Products and Relations in Symplectic Floer Homology
This paper gives a detailed and functorial treatment of products, operations and relations in Floer homology and Floer cohomology of monotone symplectic manifolds. Floer (co)homology groups were introduced by A. Floer in a series of papers [F1], [F2], [F3] and [F4]. Basic material on Floer (co)homology can also be found in [HS], [HZ], [M], [MS1], [S] and [SZ]; see also [Sch1]. Let M be a monoto...
متن کاملLagrangian Embeddings, Maslov Indexes and Integer Graded Symplectic Floer Cohomology
We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with ZΣ(L) grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin’s question for oriented, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997