Galois connections and the leray spectral sequence
نویسندگان
چکیده
منابع مشابه
The Leray-serre Spectral Sequence
Spectral sequences are a powerful bookkeeping tool, used to handle large amounts of information. As such, they have become nearly ubiquitous in algebraic topology and algebraic geometry. In this paper, we take a few results on faith (i.e., without proof, pointing to books in which proof may be found) in order to streamline and simplify the exposition. From the exact couple formulation of spectr...
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We prove in this paper a noncommutative version of Leray Theorem and then Leray-Serre Spectral Theorem for noncommutative Serre fibrations: for NC Serre fibration there are converging spectral sequences with E 2 terms as E 2 p,q = HP p (A; HP q (B, A)) =⇒ HP p+q (B) and E 2 p,q = HP p (A; Kq(B, A)) =⇒ Kp+q(B).
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A second Leray spectral sequence of relative hypercohomology is constructed. (This is skew in generality to an earlier one constructed by S. Lubkin [(1968) Ann. Math. 87, 105-255].) The Mayer-Vietoris sequence of relative hypercohomology [Lubkin, S. (1968) Ann. Math. 87, 105-255] is also generalized.
متن کاملFibered Symplectic Cohomology and the Leray-serre Spectral Sequence
We define Symplectic cohomology groups FH∗ [a,b] (E), −∞ ≤ a < b ≤ ∞ for a class of symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. When B is symplectically aspherical we construct a spectral sequence of Leray-Serre ty...
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We define Floer (or Symplectic) cohomology groups FH ]a, b] (E), −∞ ≤ a < b ≤ ∞ for a class of monotone symplectic fibrations F →֒ E −→ B with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. Our construction is a fibered extension of a construction of Viter...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1977
ISSN: 0001-8708
DOI: 10.1016/0001-8708(77)90073-1