Monodromy of torus fiber bundles and decomposability problem
  The notion of a (stably) decomposable fiber bundle is introduced. In low dimensions, for torus fiber bundles over a circle the notion translates into a property of elements of the special linear group of integral matrices. We give a complete characterization of the stably decomposable torus fiber bundle of fiber-dimension less than 4 over the circle. 
Mahir Bilen Can, Mustafa Topkara
math.AT math.GT