I know what a diffeomorphism is. But what is diffeomorphism invariance? And why is it important in physics?
E.g. it has recently been proved in algebraic geometry that rationality of surfaces is a diffeomorphism invariant.
Would this be the same as "covariant" expressions?Atheist said:Can only guess here: Since a coordinate transformation is a diffeomorphism I´d say diffeomorphism invariance is invariance under coordinate transformations.
Importance in physics thus would be obvious: Ideally, physical processes are invariant under coordinate transformations (would be a bit unpractical when physical processes depend on the coordiante system) so it´s a requirement for physical meaningfull equations.