Generalized elliptic genera and baker-Akhiezer functions

  • I. M. Krichever


Elliptic Genus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    M. F. Atiyah and F. Hirzebruch, “Spin-manifolds and group actions,” in: Essays on Topology and Related Topics, Springer-Verlag, New York (1970), pp. 18–28.Google Scholar
  2. 2.
    I. M. Krichever, “Formal groups and Atiyah-Hirzebruch formulas,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 6, 1289–1304 (1974).Google Scholar
  3. 3.
    I. M. Krichever, “Obstructions to the existence of Sl-actions. Bordisms of ramified covering spaces,” Izv. Akad. Nauk SSSR,40, No. 4, 828–844 (1976).Google Scholar
  4. 4.
    A. Hattori, “Spin-structures and Sl-actions,’ Inv. Math.,48, 7–36 (1978).Google Scholar
  5. 5.
    E. Witten, “Fermionic quantum numbers in Kaluza-Klein Theory,” in: Proceedings of the 1983 Shelter Island Conference on Quantum Field Theory and Foundations of Physics, MIT Press (1985).Google Scholar
  6. 6.
    P. S. Landweber (ed.), Elliptic Curves and Modular Forms in Algebraic Topology, Lect. Notes in Math.,1326, Springer-Verlag (1988).Google Scholar
  7. 7.
    P. S. Landweber, “Elliptic genera. An introductory overview,” in: Landweber, Op. cit.Google Scholar
  8. 8.
    S. Ochanine, “Sur les genres multiplicatifs définis par les intégrals elliptiques,” Topology,26, 143–151 (1987).Google Scholar
  9. 9.
    S. Ochanine, “Genres elliptiques équivariant,” in: Landweber, Op. cit.Google Scholar
  10. 10.
    E. Witten, “Elliptic genera and quantum field theory,” Comm. Math. Phys.,109, 525–536 (1987); E. Witten, “The index of the Dirac operator in loop space,” in: Landweber, Op. cit.Google Scholar
  11. 11.
    C. H. Taubes, “S1-action and elliptic genera,” Harvard University preprint (1987).Google Scholar
  12. 12.
    D. V. Chudnovsky and G. V. Chudnovsky, “Elliptic modular forms and elliptic genera,” Topology,27., 163–170 (1988).Google Scholar
  13. 13.
    D. Zagier, “Note on the Landweber-Strong genus,” in: Landweber, Op. cit.Google Scholar
  14. 14.
    F. Hirzebruch, “Elliptic genera of level N for complex manifolds,” Max-Planck-Institut preprint, 88–24 (1988).Google Scholar
  15. 15.
    I. M. Krichever, “Elliptic solutions of the Kadomtsev-Petviashvili equation and integratable systems of particles,” Funkts. Anal. Prilozh.,14, No. 4, 45–54 (1980).Google Scholar
  16. 16.
    “Adams operation and fixed points,” Izv. Akad. Nauk SSSR, Ser. Mat.,32, 1245–1263 (1968).Google Scholar
  17. 17.
    H. Bateman (A.Erdelyi), Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1953).Google Scholar
  18. 18.
    I. M. Krichever, “Integration of nonlinear equations using the methods of algebraic geometry,” Funkts. Anal. Prilozh.,11, No. 1, 15–31 (1977).Google Scholar
  19. 19.
    E. Kamke, Handbook of Ordinary Differential Equations [in Russian], Nauka, Moscow (1976).Google Scholar
  20. 20.
    F.Calogero, “Integrable many-body problems,” Univ. di Roma preprint,89 (1978).Google Scholar
  21. 21.
    A. Dold, “Relations between ordinary and extraordinary cohomology,” in: Colloquium on Algebraic Topology, Aarhus (1962).Google Scholar
  22. 22.
    A. S. Mischenko, “Manifolds with an action and fixed points,” Mat. Zametki,4, No. 4, 381–386 (1968).Google Scholar
  23. 23.
    G. G. Kasparov, “Invariants of classical lens spaces in bordism theory,” Izv. Nauk SSSR Ser. Mat.,33, 735–747 (1969).Google Scholar
  24. 24.
    A. S. Mischenko, “Bordisms with actions and fixed points,” Mat. Sb.,80, 307–313 (1969).Google Scholar
  25. 25.
    S. M. Gusein-Zade and I. M. Krichever, “On a formula for the fixed points of an action,” Usp. Mat. Nauk,27, No. 1, 245–246 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • I. M. Krichever
    • 1
  1. 1.Institute of Mechanics ProblemsAcademy of Sciences of the USSRMoscow

Personalised recommendations