منابع مشابه
The Equivariant Serre Spectral Sequence
For spaces with a group action, we introduce Bredon cohomology with local (or twisted) coefficients and show that it is invariant under weak equivariant homotopy equivalence. We use this new cohomology to construct a Serre spectral sequence for equivariant fibrations. Bredon [1] introduced what is now called Bredon cohomology, with the purpose of developing obstruction theory in the context of ...
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 کاملLagrangian Intersections and the Serre Spectral Sequence
For a transversal pair of closed Lagrangian submanifolds L, L of a symplectic manifold M so that π1(L) = π1(L′) = 0 = c1|π2(M) = ω|π2(M) and a generic almost complex structure J we construct an invariant with a high homotopical content which consists in the pages of order ≥ 2 of a spectral sequence whose differentials provide an algebraic measure of the highdimensional moduli spaces of pseudo-h...
متن کاملJump Loci in the Equivariant Spectral Sequence
We study the homology jump loci of a chain complex over an affine kalgebra. When the chain complex is the first page of the equivariant spectral sequence associated to a regular abelian cover of a finite-type CW-complex, we relate those jump loci to the resonance varieties associated to the cohomology ring of the space. As an application, we show that vanishing resonance implies a certain finit...
متن کاملShort Complete Proofs of the Serre Spectral Sequence Theorems
A new improved ”Simple complete proofs of the Serre spectral sequence theorems”. In ([B]) I set forth a proof of the Serre calculation of E and claimed among other things that unlike my previous attempts to prove this in graduate course lectures, this proof was routine. On presenting this material in class, I discovered it was not as routine as I had imagined. With the help of Pallavi Jayawart ...
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: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1993-1123662-9