Spectral Sequences arising in Differential Geometry
Spencer cohomology groups are used in both the formal theory of partial
differential equations and the theory of exterior differential systems
in order to provide qualitative statements about the space of solutions
on the basis of symbolic calculus only. In particular several obstructions
to integrability are known to live in Spencer cohomology. We will interprete
Spencer cohomology as the E1-term
of a spectral sequence, which in contrast to Spencer cohomology itself
depends in general on the particular application. Quite remarkbly the limit
of this spectral sequence is known in advance in many applications,
and it is really the way it converges to this limit that provides relevant
geometric data.
Fall
2001 meeting of the PNGS