Fröhlicher spectral sequence
Encyclopedia
In mathematics
, the Fröhlicher spectral sequence is a tool in the theory of complex manifold
s, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifold
s. A spectral sequence
is set up, the degeneration of which would give the results of Hodge theory
and Dolbeault's theorem.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the Fröhlicher spectral sequence is a tool in the theory of complex manifold
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic....
s, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifold
Kähler manifold
In mathematics, a Kähler manifold is a manifold with unitary structure satisfying an integrability condition.In particular, it is a Riemannian manifold, a complex manifold, and a symplectic manifold, with these three structures all mutually compatible.This threefold structure corresponds to the...
s. A spectral sequence
Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations...
is set up, the degeneration of which would give the results of Hodge theory
Hodge theory
In mathematics, Hodge theory, named after W. V. D. Hodge, is one aspect of the study of the algebraic topology of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised...
and Dolbeault's theorem.