Categorical differential geometry

M. V. Losik

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1994)

  • Volume: 35, Issue: 4, page 274-290
  • ISSN: 1245-530X

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Losik, M. V.. "Categorical differential geometry." Cahiers de Topologie et Géométrie Différentielle Catégoriques 35.4 (1994): 274-290. <http://eudml.org/doc/91549>.

@article{Losik1994,
author = {Losik, M. V.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {differential space; formal differential geometry; diffeological spaces; Gelfand-Fuks cohomology; infinite-dimensional manifolds; concrete quasi- toposes},
language = {eng},
number = {4},
pages = {274-290},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Categorical differential geometry},
url = {http://eudml.org/doc/91549},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Losik, M. V.
TI - Categorical differential geometry
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1994
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 35
IS - 4
SP - 274
EP - 290
LA - eng
KW - differential space; formal differential geometry; diffeological spaces; Gelfand-Fuks cohomology; infinite-dimensional manifolds; concrete quasi- toposes
UR - http://eudml.org/doc/91549
ER -

References

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  1. 1 Bernstein I.N., Rosenfeld B.A., Homogeneous spaces of infinite dimensional Lie algebras and characteristic classes of foliations, Uspehi Mat. Nauk28, 4 (1973), 103-138. (Russian) Zbl0285.57014MR415633
  2. 2 Bott R., Haefliger A., On characteristic classes of Γ-foliations, Bull. Amer. Math. Soc.78 (1972), 1039-104. Zbl0262.57010
  3. 3 Bouma L.C., Van Est W.T., Manifold schemes and foliations on the 2-torus and the Klein bottle, Proc.Kon.Ned.Akad.Wet., Amsterdam, série A81, 3 (1978), 313-347. Zbl0393.57008
  4. 4 Frölicher A., Kriegl A., Linear spaces and differentiation theory, John Wiley & Sons, Chichester. New York. Brisbane. Toronto. Singapore, 1988. Zbl0657.46034MR961256
  5. 5 Gel'fand I.M., Feigin, Fuks D.B., Cohomology of the Lie algebra of formal vector fields with coefficients in its dual space and variations of characteristic classes of foliations, Functional. Anal. i Prilozhen.8, 2 (1974), 13-29. (Russian) Zbl0298.57011MR356082
  6. 6 Losik M.V., Characteristic classes of structures on manifolds, Functional. Anal. i Prilozhen.21, 3 (1987), 38-52; English transl. in Functional Anal. Appl.21 (1987), 206-216. Zbl0649.57024MR911773
  7. 7 Losik M.V., Some generalization of manifold and its characteristic classes, Functional. Anal. i Prilozhen.24,1 (1990), 29-37; English transl. in Functional Anal. Appl.24 (1990), 26-32. Zbl0714.57012MR1052265
  8. 8 Losik M.V., Fréchet manifolds as diffeological spaces, Soviet Math. (Iz. vuz)5 (1992), 36-42. (Russian) Zbl0774.58002
  9. 9 Michor P.W., Manifolds of Differentiable Mappings, Shiva Mathematics Series, 1980. Zbl0433.58001
  10. 10 Michor P.W., A convenient setting for differential geometry and global analysis, Cahiers de topologie et géométrie différentielle catégoriquesXXV, 1, 2 (1984), 63-109; 113-187. Zbl0548.58001
  11. 11 Molino P., Riemannian foliations, Birkhäuser, Boston. Basel, 1988. Zbl0633.53001
  12. 12 Pasternack J., Foliations and compactLie group actions, Comment. Math. Helv.46 (1971), 467-477. Zbl0228.57020
  13. 13 Pradines J., Un example de feuilletage sans holonomie dont l'espace des feuilles n'est par une Q-variété, C.R. Ac. Sci.Paris288 (1979), 245-248. Zbl0402.57016
  14. 14 Reinhart B., Harmonic integrals on foliated manifolds, Amer. Jour. of Math.81 (1959), 527-536. Zbl0088.07902
  15. 15 Satake I., On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. USA42 (1956), 359-363. Zbl0074.18103
  16. 16 Souriau J.-M., Groups différentiels et physique mathématique, Feuilletages et quantification géométrique, Coll. Travaux en Cours, Hermann, Paris, 1984, pp. 75-79. Zbl0541.58002
  17. 17 Van Est W.T., Rapport sur les S-atlas, Astérisque116, 235-292. Zbl0543.58003
  18. 18 Veblen O., Invariants of quadratic Differential Forms, Cambridge Tracts, 1927. JFM53.0681.01

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