### A new cohomology for the Morse theory of strongly indefinite functionals on Hilbert spaces

#### Abstract

A generalized cohomology, similar to Szulkin's cohomology but with more

general functorial properties, is constructed. This theory is used to

define a relative Morse index and to prove relative Morse relations for

strongly indefinite functionals on Hilbert spaces.

general functorial properties, is constructed. This theory is used to

define a relative Morse index and to prove relative Morse relations for

strongly indefinite functionals on Hilbert spaces.

#### Keywords

generalized cohomology; Morse index; Morse relations; strongly indefinite functionals

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