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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 14th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something, not done yet but need to save <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/1">v1</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   starting something, not done yet but need to save

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2020
   • (edited Nov 16th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the original articles: *** The statement, with a [[string theory]]-motivated plausibility argument, is due to * [[Edward Witten]], _Elliptic genera and quantum field theory_, Comm. Math. Phys. Volume 109, Number 4 (1987), 525-536. ([euclid:cmp/1104117076](http://projecteuclid.org/euclid.cmp/1104117076)) The first [[proof]] was given in * [[Clifford Taubes]], _$S^1$-actions and elliptic genera_, Comm. Math. Phys. Volume 122, Number 3 (1989), 455-526 ([euclid:cmp/1104178471](https://projecteuclid.org/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](https://doi.org/10.2307/1990915)) 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](https://doi.org/10.1007/978-1-4613-0729-7_2)) <a href="https://ncatlab.org/nlab/revision/diff/rigidity+theorem+for+elliptic+genera/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/2">v2</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   added pointer to the original articles:

   ---

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

   • Edward Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. Volume 109, Number 4 (1987), 525-536. (euclid:cmp/1104117076)

   The first proof was given in

   • Clifford Taubes, $S^1$-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

   • 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)

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso this one: * [[Friedrich Hirzebruch]], _Elliptic Genera of Level $N$ 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](https://doi.org/10.1007/978-94-015-7809-7_3)) <a href="https://ncatlab.org/nlab/revision/diff/rigidity+theorem+for+elliptic+genera/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/3">v3</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   also this one:

   • Friedrich Hirzebruch, Elliptic Genera of Level $N$ 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)

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexas well as this one: * 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](https://doi.org/10.1007/BF01156822)) <a href="https://ncatlab.org/nlab/revision/diff/rigidity+theorem+for+elliptic+genera/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/3">v3</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   as well as this one:

   • 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)

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2020
   • (edited Nov 16th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexand this one: * [[Kefeng Liu]], _On elliptic genera and theta-functions_, Topology Volume 35, Issue 3, July 1996, Pages 617-640 (<a href="https://doi.org/10.1016/0040-9383(95)00042-9">doi:10.1016/0040-9383(95)00042-9</a>) <a href="https://ncatlab.org/nlab/revision/diff/rigidity+theorem+for+elliptic+genera/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/3">v3</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   and this one:

   • 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)

   diff, v3, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 17th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this pointer: * [[Kefeng Liu]], _On modular invariance and rigidity theorems_, J. Differential Geom. Volume 41, Number 2 (1995), 343-396 ([euclid:jdg/1214456221](https://projecteuclid.org/euclid.jdg/1214456221)) <a href="https://ncatlab.org/nlab/revision/diff/rigidity+theorem+for+elliptic+genera/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/rigidity+theorem+for+elliptic+genera/5">v5</a>, <a href="https://ncatlab.org/nlab/show/rigidity+theorem+for+elliptic+genera">current</a>

   added this pointer:

   • Kefeng Liu, On modular invariance and rigidity theorems, J. Differential Geom. Volume 41, Number 2 (1995), 343-396 (euclid:jdg/1214456221)

   diff, v5, current