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Complex cobordism ring and conformal field theory over Z

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  • [A] Adams, J.F.: Stable homotopy and generalized homology. Chicago Lectures in Math. Chicago: Univ. Chicago Press 1974

    Google Scholar 

  • [BeSc] Beilinson, A.A., Schechtman, V.A.: Determinant bundles and Virasoro algebras. Commun. Math. Phys.118, 651–701 (1988)

    Google Scholar 

  • [BuSh] Bukshtaber, V.M., Shokurov, A.V.: The Landweber-Novikov algebra and formal vector fields on the line. Funct. Anal. Appl.12, 159–168 (1978)

    Google Scholar 

  • [DJKM] Date, E., Jimbo, M., Kashiwara, M., Miwa, T.: Transformation groups for soliton equations. In: Jimbo, M., Miwa, T., (eds.) Proceedings of RIMS Symposium Non-linear integrable systems — classical theory and quantum theory. Kyoto, pp. 39–119, Singapore: World Scientific 1983

    Google Scholar 

  • [Haz] Hazewinkel, M.: Formal groups and applications. Boston Orlando: Academic Press 1978

    Google Scholar 

  • [Hir1] Hirzebruch, F.: Topological methods in algebraic geometry, 3rd edn. Berlin Heidelberg New York: Springer 1966

    Google Scholar 

  • [Hir2] Hirzebruch, F.: Elliptic genera of levelN for complex manifolds. Preprint MPI/88-24

  • [KSU1] Katsura, T., Shimizu, Y., Ueno, K.: New bosonization and conformal field theory over Z. Commun. Math. Phys.121, 603–622 (1988)

    Google Scholar 

  • [KSU2] Katsura, T., Shimizu, Y., Ueno, K.: Formal groups and conformal field theory overZ. Adv. Stud. Pure Math.19, 347–366 (1989)

    Google Scholar 

  • [KNTY] Kawamoto, N., Namikawa, Y., Tsuchiya, A., Yamada, Y.: Geometric realization of conformal field theory on Riemann surfaces. Commun. Math. Phys.116, 247–308 (1988)

    Google Scholar 

  • [Kr] Krichever, I.M.: Generalized elliptic genera and Baker-Akhiezer functions. Preprint 1989

  • [La] Landweber, P., (ed.): Elliptic curves and modular forms in algebraic topology (Lecture Notes in Math., Vol. 1326). Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [La2] Landweber, P.S.: Associated prime ideals and Hopf algebras. J. Pure Appl. Algebra3, 43–58 (1973)

    Google Scholar 

  • [Li] Littlewood, D.E.: The theory of group characters and matrix representation of groups. Oxford: Oxford University Press 1950

    Google Scholar 

  • [MiSt] Milnor, J.W., Stasheff, J.D.: Characteristic classes. Ann. Math. Stud.76 (1974)

  • [Mo] Morava, J.: On the complex cobordism ring as a Fock representation. In: Mimura, M. (ed.) Homotopy theory and related topics. Proceedings, Kinosaki 1987 (Lecture Notes Math. Vol. 1418, pp. 184–204) Berlin Heidelberg New York: Springer 1988

    Google Scholar 

  • [MoSh] Morava, J., Shimizu, Y.: A topological generalization of the elliptic genus. Preprint 1990

  • [S] Sato, M.: Soliton equations as dynamical systems on an infinite dimensional Grassmann manifold. Sūriken-Kōkyūroku439, 30–46 (1981)

    Google Scholar 

  • [SM] Sato, M.: Lectures on KP equations (in Japanese). Notes by Mulase, M.

  • [SN] Sato, M., Noumi, M.: Soliton equations and universal Grassmann manifold. Sophia Univ. Kōkyūroku in Math.18 (1984)

  • [Sh] Shiota, T.: Characterization of Jacobian varieties in terms of soliton equations. Invent. Math.83, 333–382 (1986)

    Google Scholar 

  • [T] Tamanoi, H.: Hyperelliptic genera. Thesis, The Johns Hopkins Univ. 1987

  • [TK] Tsuchiya, A., Kanie, Y.: Fock space representation of the Virasoro algebra —Intertwining operators. Publ. RIMS Kyoto Univ.22, 259–327 (1986)

    Google Scholar 

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Partially supported by Max-Planck-Institut für Mathematik

Partially supported by Grant-in-Aid, Ministry of Education of Japan

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Katsura, T., Shimizu, Y. & Ueno, K. Complex cobordism ring and conformal field theory over Z. Math. Ann. 291, 551–571 (1991).

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  • Field Theory
  • Conformal Field Theory
  • Cobordism Ring
  • Complex Cobordism