FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 6, PAGES 141-175

**Multiplicative $A$**_{¥}-structure in terms of
spectral sequences of fibrations

S. V. Lapin

Abstract

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In the present paper, the technique of spectral sequences with
$A$_{¥}-structures in
their terms is developed for differential algebras with filtrations.
Applications of this technique to the multiplicative spectral
sequences of fibrations are given.
We show that if the base of fibration is connected and simply
connected, then the structure graded $A$_{¥}-algebra in the
second term of the spectral sequence of a fibration is the tensor
product of the cohomology $A$_{¥}-algebra of the
base and the cohomology $A$_{¥}-algebra of the
fibre of this fibration.

Location: http://mech.math.msu.su/~fpm/eng/k08/k086/k08609h.htm

Last modified: June 4, 2009