RELATIVE LERAY NUMBERS VIA SPECTRAL SEQUENCES
نویسندگان
چکیده
Let F be a fixed field and let X simplicial complex on the vertex set V. The Leray number L ( ; ) is minimal d such that for all i ⩾ S ⊂ V , induced [ ] satisfies H ∼ = 0 . numbers play role in formulating proving topological Helly-type theorems. For two complexes Y same V, define relative as ∖ τ ∈ In this paper we extend colorful Helly theorem to setting. Our main tool spectral sequence intersection of indexed by geometric lattice.
منابع مشابه
Second Leray spectral sequence of relative hypercohomology.
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 کاملThe 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...
متن کامل1 Leray Spectral Sequence Theorem for Nccw
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).
متن کاملLeray in Oflag XVIIA: The origins of sheaf theory, sheaf cohomology, and spectral sequences
Jean Leray (November 7, 1906–November 10, 1998) was confined to an officers’ prison camp (“Oflag”) in Austria for the whole of World War II. There he took up algebraic topology, and the result was a spectacular flowering of highly original ideas, ideas which have, through the usual metamorphism of history, shaped the course of mathematics in the sixty years since then. Today we would divide his...
متن کاملLeray Numbers of Projections and a Topological Helly Type Theorem
Let X be a simplicial complex on the vertex set V . The rational Leray number L(X) of X is the minimal d such that H̃i(Y ;Q) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Suppose V = ⋃m i=1 Vi is a partition of V such that the induced subcomplexes X[Vi] are all 0-dimensional. Let π denote the projection of X into the (m − 1)-simplex on the vertex set {1, . . . ,m} given by π(v) = i if v ∈ Vi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematika
سال: 2021
ISSN: ['2041-7942', '0025-5793']
DOI: https://doi.org/10.1112/mtk.12103