Deformation of a 3 -> 3 Pachner move relation capturing exotic second   homologies
  A new relation in Grassmann algebra is presented, corresponding naturally to the four-dimensional Pachner move 3 -> 3. This relation is obtained by deforming a known relation associated with an exotic chain complex built for a triangulated four-manifold. The possible deformation terms turn out to correspond to second (middle) homologies of one more exotic complex. Both sides of the new relation are nonlinear in the deformation: they contain terms of degrees 0, 1 and 2. 
Igor Korepanov
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