(…)
The statement, with a string theory-motivated plausibility argument, is due to
The first proof was given in
Clifford Taubes, -actions and elliptic genera, Comm. Math. Phys. Volume 122, Number 3 (1989), 455-526 (euclid:cmp/1104178471)
Raoul Bott, Clifford Taubes, On the Rigidity Theorems of Witten, Journal of the American Mathematical Society Vol. 2, No. 1 (Jan., 1989), pp. 137-186 (doi:10.2307/1990915)
Review in
Further proofs:
Friedrich Hirzebruch, Elliptic Genera of Level 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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