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  • Bott
  • In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by Raoul Bott (1957, 1959), which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres. (wikipedia.org)
  • Bott periodicity can be formulated in numerous ways, with the periodicity in question always appearing as a period-2 phenomenon, with respect to dimension, for the theory associated to the unitary group. (wikipedia.org)
  • The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres. (wikipedia.org)
  • What Bott periodicity offered was an insight into some highly non-trivial spaces, with central status in topology because of the connection of their cohomology with characteristic classes, for which all the (unstable) homotopy groups could be calculated. (wikipedia.org)
  • One formulation of Bott periodicity describes the twofold loop space, Ω2BU of BU. (wikipedia.org)
  • theory
  • She was quite instrumental in disproving the theory of functional periodicity, which was widely believed to be true by scientists as well as the general public. (wikipedia.org)
  • Note that octaves are usually ignored in constructing periodicity blocks (as they are in scale theory generally) because it is assumed that for any pitch in the tuning system, all pitches differing from it by some number of octaves are also available in principle. (wikipedia.org)
  • study
  • At the end of the program, she decided to study functional periodicity for her dissertation research. (wikipedia.org)
  • In a paper published in EPJ B , the authors study how the crystal periodicity affects the motion of ions whose energy belongs to a 1 to 2 MeV range, as they are transmitted through very thin crystals on the order of a few hundred nanometres, and how it impacts their angular distribution. (eurekalert.org)
  • Physical
  • Functional periodicity is a term that emerged around the late 19th century around the belief, later to be found invalid, that women suffered from physical and mental impairment during their menstrual cycle. (wikipedia.org)
  • case
  • Frequently, it forms a cyclic group, in which case identifying the m pitches of the periodicity block with m-equal tuning gives equal tuning approximations of the just ratios that defined the original lattice. (wikipedia.org)