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A new relation in Grassmann algebra is presented, corresponding naturally tothe four-dimensional Pachner move 3 -> 3. This relation is obtained bydeforming a known relation associated with an exotic chain complex built for atriangulated four-manifold. The possible deformation terms turn out tocorrespond to second (middle) homologies of one more exotic complex. Both sidesof the new relation are nonlinear in the deformation: they contain terms ofdegrees 0, 1 and 2.

Deformation of a 3 -> 3 Pachner move relation capturing exotic second homologies