In mathematics, the Frölicher spectral sequence (often misspelled as Fröhlicher) is a tool in the theory of complex manifolds, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifolds. It was introduced by Frölicher (1955). A spectral sequence is set up, the degeneration of which would give the results of Hodge theory and Dolbeault's theorem.