A note on Atiyah's $\Gamma$-index theorem in Heisenberg calculus
  In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's $\Gamma$-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial $\Gamma$-index. 
Tatsuki Seto
math.DG math.KT