Arnold's spectral sequence
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In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function to canonical form near critical points. It was introduced by Vladimir Arnold in 1975.[1][2][3]
Definition
It is a spectral sequence for the filtered de Rham complex with
- The filtration coming from increasing order of poles along discriminant loci (Diagonals)
- E1-page has differential forms that have logarithmic singularities along the diagonals
- The differential encodes the relationships among the singular forms[4]
