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Let  X  be a compact quotient of the product of the real Heisenberg group  H  4 m +1  of dimension 4 m  + 1 and the three-dimensional real Euclidean space  R  3 . A left-invariant hypercomplex structure on  H  4 m +1  ×  R  3  descends onto the compact quotient  X . The space  X  is a hyperholomorphic fibration of 4-tori over a 4 m -torus. We calculate the parameter space and obstructions to deformations of this hypercomplex structure on  X . Using our calculations, we show that all small deformations generate invariant hypercomplex structures on  X  but not all of them arise from deformations of the lattice. This is in contrast to the deformations on the 4 m -torus.

DEFORMATIONS OF HYPERCOMPLEX STRUCTURES ASSOCIATED TO HEISENBERG GROUPS