Topological Charge of Lattice Abelian Gauge Theory
  Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle. 
T. Fujiwara, H. Suzuki and K. Wu (Ibaraki U., Mito)