nLab rigidity theorem for elliptic genera






The statement, with a string theory-motivated plausibility argument, is due to

The first proof was given in

Review in

  • Raoul Bott, On the Fixed Point Formula and the Rigidity Theorems of Witten, Lectures at Cargése 1987. In: ’t Hooft G., Jaffe A., Mack G., Mitter P.K., Stora R. (eds) Nonperturbative Quantum Field Theory. NATO ASI Series (Series B: Physics), vol 185. Springer (1988) (doi:10.1007/978-1-4613-0729-7_2)

Further proofs:

  • Friedrich Hirzebruch, Elliptic Genera of Level NN for Complex Manifolds, In: Bleuler K., Werner M. (eds) Differential Geometrical Methods in Theoretical Physics NATO ASI Series (Series C: Mathematical and Physical Sciences), vol 250. Springer (1988) (doi:10.1007/978-94-015-7809-7_3)

  • I. M. Krichever, Generalized elliptic genera and Baker-Akhiezer functions, Mathematical Notes of the Academy of Sciences of the USSR 47, 132–142 (1990) (doi:10.1007/BF01156822)

  • Kefeng Liu, On modular invariance and rigidity theorems, J. Differential Geom.

    Volume 41, Number 2 (1995), 343-396 (euclid:jdg/1214456221)

  • Kefeng Liu, On elliptic genera and theta-functions, Topology Volume 35, Issue 3, July 1996, Pages 617-640 (doi:10.1016/0040-9383(95)00042-9)

  • Anand Dessai, Rainer Jung, On the Rigidity Theorem for Elliptic Genera, Transactions of the American Mathematical Society Vol. 350, No. 10 (Oct., 1998), pp. 4195-4220 (26 pages) (jstor:117694)

  • Ioanid Rosu, Equivariant Elliptic Cohomology and Rigidity, American Journal of Mathematics 123 (2001), 647-677 (arXiv:math/9912089)

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