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Original Articles

Diffeological Clifford algebras and pseudo-bundles of Clifford modules

Pages 1785-1828 | Received 14 Jun 2016, Accepted 23 Apr 2018, Published online: 15 May 2018

References

  • Souriau JM. Groups différentiels. Differential geometrical methods in mathematical physics (Proc. Conf., Aix-en-Provence/Salamanca, 1979). Vol. 836, Lecture notes in mathematics. Berlin: Springer; 1980. p. 91–128.
  • Souriau JM. Groups différentiels de physique mathématique. South Rhone seminar on geometry, II (Lyon, 1984). Astérisque; Numéro Hors Série; 1985 p. 341–399.
  • Iglesias-Zemmour P. Diffeology. Vol. 185, Mathematical surveys and monographs. AMS: Providence (RI); 2013.
  • Várilly JC. An introduction to noncommutative geometry. EMS series of lectures in mathematics; Zurich: EMS publishing house; 2006.
  • Iglesias-Zemmour P. Diffeology of the infinite Hopf fibrations. In: Kubarsi J., Pradines J., Wolak R., Rybicki T. editors. Geometry and topology of manifolds. Vol. 76, Polish Academy of Science Institute of Mathematics. Warsaw: Banach Center Publications; 2007. p. 349–393.
  • Vincent M. Diffeological differential geometry [master thesis]. Copenhagen: University of Copenhagen; 2008.
  • Christensen JD, Wu E. Tangent spaces and tangent bundles for diffeological spaces, arXiv:1411.5425v1.
  • Christensen JD, Sinnamon G, Wu E. The D-topology for diffeological spaces. Pac J Math. 2014;272:87–110.
  • Wu E. Homological algebra for diffeological vector spaces. Homol Homotopy Appl. 2015;17:339–376.
  • Pervova E. On the notion of scalar product for finite-dimensional diffeological vector spaces. Electr J Linear Algebra. 2018;34:18–27.
  • Roe J. Elliptic operators, topology and asymptotic methods. 2nd ed. Vol. 395, Boca Raton London New York Washington DC: Chapman & Hall/CRC. 2001.
  • Pervova E. Multilinear algebra in the context of diffeology, arXiv:1504.08186v2.
  • Pervova E. Diffeological vector pseudo-bundles. Topol Appl. 2016;202:269–300.
  • Pervova E. Diffeological gluing of vector pseudo-bundles and pseudo-metrics on them. Topol Appl. 2017;220:65–99.
  • Ntumba P. DW complexes and their underlying topological spaces. Quaestiones Math. 2002;25:119–134.
  • Pervova E. Pseudo-bundles of exterior algebras as diffeological Clifford modules. Adv Appl Clifford Algebras. 2017;27:2677–2737.
  • Watts J. Diffeologies, differential spaces, and symplectic geometry [PhD thesis]. Canada: University of Toronto; 2012.

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