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On the Geometry and Topology of the Commutator of Unit Quaternions

In: Advances in Mathematics and Applications

Author

Listed:
  • Alcibiades Rigas

    (University of Campinas, Institute of Mathematics, Statistics and Scientific Computing)

  • Dan A. Agüero Cerna

    (University of Campinas, Institute of Mathematics, Statistics and Scientific Computing)

Abstract

This is a narrative rather than a survey of the research relevant to the subject of the title, done basically at IMECC, Unicamp, from 1982 to 2005. Many people, including students, as well as the first author, contributed. The second author compiled the material in his master’s dissertation (Cerna, On the geometry and topology of the commutator of unit quaternions. Master’s Dissertation, IMECC, Unicamp, 2016) and he is not responsible for imprecisions, for forgetting to give credit where due, etc. We consider known a little basic homotopy, like the exact sequence of a fibration, a few basic homotopy groups of spheres, and the Bott periodicity for Spin, U, and Sp, and also basic definitions of Riemannian geometry.

Suggested Citation

  • Alcibiades Rigas & Dan A. Agüero Cerna, 2018. "On the Geometry and Topology of the Commutator of Unit Quaternions," Springer Books, in: Carlile Lavor & Francisco A. M. Gomes (ed.), Advances in Mathematics and Applications, pages 275-299, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-94015-1_12
    DOI: 10.1007/978-3-319-94015-1_12
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