| In ergodic theory, cohomological questions appear at many places. For example in the construction of some Schroedinger operators (PDF file) with a theorem of Feldman and Moore (PDF file) . |
Maybe the simplest cohomology group is defined for an automorphism
T: X -> X of a Lebesgue space (X,A,m).
The group of measurable sets A (with symmetric difference + as groupoperation)
modulo the subgroup { Z = Y + T(Y) } of all coboundaries is the first
cohomology group of the Z action with structure group
Z 2 .
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