Deformations of hypercomplex structures associated to Heisenberg groups

Gueo Grantcharov Henrik Pedersen Yat Sun Poon

Complex Variables and Complex Analysis mathscidoc:1910.43827

Quarterly Journal of Mathematics, 59, (3), 335-362, 2008.9
Let X be a compact quotient of the product of the real Heisenberg group H <sub>4m+1</sub> of dimension 4m + 1 and the three-dimensional real Euclidean space R <sup>3</sup> . A left-invariant hypercomplex structure on H <sub>4m+1</sub> R <sup>3</sup> descends onto the compact quotient X. The space X is a hyperholomorphic fibration of 4-tori over a 4m-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 4m-torus.
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@inproceedings{gueo2008deformations,
  title={Deformations of hypercomplex structures associated to Heisenberg groups},
  author={Gueo Grantcharov, Henrik Pedersen, and Yat Sun Poon},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020221516652226356},
  booktitle={Quarterly Journal of Mathematics},
  volume={59},
  number={3},
  pages={335-362},
  year={2008},
}
Gueo Grantcharov, Henrik Pedersen, and Yat Sun Poon. Deformations of hypercomplex structures associated to Heisenberg groups. 2008. Vol. 59. In Quarterly Journal of Mathematics. pp.335-362. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020221516652226356.
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