The Aharonov-Bohm effect is a quantum mechanical phenomenon where electrons passing through a region of vanishing magnetic field get scattered due to topological effects. It turns out that this phenomenon is closely related to the cohomology of forms with integer coefficients. We study this relationship from the point of view of the Calderón problem and see that it can be captured in how Cauchy data of the connection Laplacian determines uniquely the holonomy representation of the connection.
The work was partially supported by Finnish Academy of Science and by NSF Grant No. DMS-0807502