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Why is space three-dimensional and how may groups be seen?


First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky ‘three-channel theorem’, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H 1, ..., Hs of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.

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Vinogradov, A.M. Why is space three-dimensional and how may groups be seen?. Acta Appl Math 5, 169–180 (1986).

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AMS (MOS) subject classifications (1980)

  • 94A99
  • 92A27
  • 20F32
  • 20C99

Key words

  • Tolerance space
  • visual perception
  • group crystal
  • Burnside problem