The leray spectral sequence of a mapping for generalized cohomology

1971 ◽  
Vol 24 (1) ◽  
pp. 53-70
Author(s):  
Richard N. Cain
Keyword(s):  
Spectral Sequence ◽  
Leray Spectral Sequence ◽  
Generalized Cohomology

EQUIVARIANT POISSON COHOMOLOGY AND A SPECTRAL SEQUENCE ASSOCIATED WITH A MOMENT MAP

1999 ◽  
Vol 10 (08) ◽  
pp. 977-1010 ◽  
Author(s):  
VIKTOR L. GINZBURG
Keyword(s):  
Tensor Product ◽  
Spectral Sequence ◽  
Vector Fields ◽  
Equivariant Cohomology ◽  
Poisson Manifold ◽  
Momentum Mapping ◽  
Poisson Cohomology ◽  
Leray Spectral Sequence ◽  
Differential Complex ◽  
Extensive Introduction

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the E2-term equal to the tensor product of the cohomology of the Lie algebra and the equivariant Poisson cohomology of the manifold. The latter is defined as the equivariant cohomology of the multi-vector fields made into a G-differential complex by means of the momentum mapping. An extensive introduction to equivariant cohomology of G-differential complexes is given including some new results and a number of examples and applications are considered.

scholarly journals A LERAY SPECTRAL SEQUENCE FOR NONCOMMUTATIVE DIFFERENTIAL FIBRATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350015 ◽  
Author(s):  
EDWIN BEGGS ◽  
IBTISAM MASMALI
Keyword(s):  
Spectral Sequence ◽  
Sheaf Cohomology ◽  
Left Module ◽  
Graded Algebras ◽  
Serre Spectral Sequence ◽  
Differential Graded Algebras ◽  
Zero Curvature ◽  
Total Differential ◽  
Leray Spectral Sequence ◽  
Special Case

This paper describes the Leray spectral sequence associated to a differential fibration. The differential fibration is described by base and total differential graded algebras. The cohomology used is noncommutative differential sheaf cohomology. For this purpose, a sheaf over an algebra is a left module with zero curvature covariant derivative. As a special case, we can recover the Serre spectral sequence for a noncommutative fibration.

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