Topological invariants for closed hypersurfaces
  We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion that depends on the geometry of the manifold and the ambient space. We use these quantities to find obstructions to the existence of certain codimension one foliations. 
\'Icaro Gon\c{c}alves, Eduardo Longa
math.DG