Contents

cohomology

# Contents

## Idea

The de Rham cohomology and Dolbeault cohomology can be viewed as abelian sheaf cohomology theories with coefficients in the sheaf of locally constant functions, respectively holomorphic functions. Spencer cohomology is a generalization of these two cohomologies for the case of the solution sheaf of an arbitrary linear differential operator.

## References

### General

Discussion of Spencer cohomology as the home of the higher-order torsion invariants of G-structures originates in

• Victor Guillemin, The integrability problem for $G$-structures, Trans. Amer. Math. Soc. 116 (1965), 544–560. (JSTOR)

### In classification of SuGra backgrounds

On Spencer cohomology applied to the classification of BPS solutions of D=11 supergravity:

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