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The index of the dirac operator in loop space

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1326))

Research supported in part by NSF Grants PHY80-19754 and 86-16129

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References

  1. E. Witten, J. Diff. Geom. 17 (1982) 661; and in Anomalies, Geometry, and Topology, ed. W. Bardeen and A. White (World Scientific, 1985), especially pp. 91–95.

    Google Scholar 

  2. A. Schellekens and N. Warner, Phys. Lett. 177B (1986) 317, “Anomaly Cancellation and Self-Dual Lattices” (MIT preprint, 1986), “Anomalies, Characters, and Strings” (CERN preprint TH-4529/86); K. Pilch, A. Schellekens, and N. Warner (preprint, 1986).

    Article  MathSciNet  Google Scholar 

  3. E. Witten, “Elliptic Genera and Quantum Field Theory” (Princeton preprint PUPT-1024, 1986), to appear in Comm. Math. Phys.

    Google Scholar 

  4. A. Pressley and G.B. Segal, Loop Groups and Their Representations (Oxford University Press, 1986).

    Google Scholar 

  5. M.F. Atiyah and I. Singer, Ann. Math. 87 (1968) 484, 586

    Article  MathSciNet  Google Scholar 

  6. M.F. Atiyah and G.B. Segal, Ann. Math. 87 (1968) 531.

    Article  MathSciNet  Google Scholar 

  7. E. Witten, “Physics and Geometry,” address at the International Congress of Mathematicians, Berkeley, August 1986, section IV.

    Google Scholar 

  8. G. Moore and P. Nelson, Phys. Rev. Lett. 53 (1984) 1519.

    Article  MathSciNet  Google Scholar 

  9. T. Killingback, “World Sheet Anomalies and Loop Geometry,” Princeton preprint (1986).

    Google Scholar 

  10. I.B. Frenkel, “Spinor Representations of Affine Lie Algebras,” Proc. Nat. Acad. Sci. USA 77 (1980) 6303; “Two Constructions of Affine Lie Algebra Representations,” J. Funct. Anal. 44 (1981) 259.

    Article  MathSciNet  MATH  Google Scholar 

  11. M.F. Atiyah and F. Hirzebruch, in Essays in Topology and Related Subjects (Springer-Verlag, 1970), p. 18.

    Google Scholar 

  12. E. Witten, “Fermion Quantum Numbers in Kaluza-Klein Theory,” in the Proceedings of the 1983 Shelter Island Conference on Quantum Field Theory and the Foundations of Physics, eds. N. Khuri et al. (MIT Press, 1985).

    Google Scholar 

  13. P. Landweber and R.E. Stong, “Circle Actions on Spin Manifolds and Characteristic Numbers,” Rutgers preprint (1985), to appear in Topology; P. Landweber, “Elliptic Cohomology and Modular Forms,” to appear in this volume.

    Google Scholar 

  14. S. Ochanine, “Sur les genres multiplicatifs définis par des intégrales elliptiques,” to appear in Topology; “Genres Elliptiques Equivariantes,” to appear in this volume.

    Google Scholar 

  15. D. V. and G. V. Chudnovsky, “Elliptic Modular Forms and Elliptic Genera,” Columbia University preprint (1985), to appear in Topology.

    Google Scholar 

  16. D. Zagier, “Note on the Landweber-Stong Elliptic Genus,” to appear in this volume.

    Google Scholar 

  17. A. Hattori, “Spin Structures and S 1 Actions,” Inv. Math. 48 (1978) 7.

    Article  MathSciNet  MATH  Google Scholar 

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Peter S. Landweber

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© 1988 Springer-Verlag

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Witten, E. (1988). The index of the dirac operator in loop space. In: Landweber, P.S. (eds) Elliptic Curves and Modular Forms in Algebraic Topology. Lecture Notes in Mathematics, vol 1326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078045

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  • DOI: https://doi.org/10.1007/BFb0078045

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