On bi-hamiltonian geometry of the Lagrange top
  We consider three different incompatible bi-Hamiltonian structures for the Lagrange top, which have the same foliation by symplectic leaves. These bivectors may be associated with the different 2-coboundaries in the Poisson-Lichnerowicz cohomology defined by canonical bivector on $e^*(3)$. 
A. V. Tsiganov