Can nonlocal Dirac operators be topologically proper ?
  By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. 
Ting-Wai Chiu (National Taiwan University)