Given an unital pre-$C^*$ algebra $B$ with a $*$-exterior algebra, one can define extended diffeomorphism group for the noncommutative manifold $B$ and its subgroup of topologically trivial elements. Using results of Bratteli–Elliott–Jorgensen and Krähmer, we compute these groups when $B$ is an irrational noncommutative $2$-torus and the algebraic standard Podleś sphere, respectively. We then apply this to the computation of moduli spaces of solutions to Euclidean Maxwell’s equations with fixed topological sector and current $1$-form.

This is joint work with B. Ćaćić.