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Rigidity of elliptic genera for nonspin manifolds

Michael Wiemeler

Algebraic & Geometric Topology 25 (2025) 2083–2097
Bibliography
1 M Amann, A Dessai, The Â-genus of S1-manifolds with finite second homotopy group, C. R. Math. Acad. Sci. Paris 348 (2010) 283 MR2600123
2 M Atiyah, F Hirzebruch, Spin-manifolds and group actions, from: "Essays on topology and related topics", Springer (1970) 18 MR278334
3 L D Borsari, Bordism of semifree circle actions on Spin manifolds, Trans. Amer. Math. Soc. 301 (1987) 479 MR882700
4 R Bott, C Taubes, On the rigidity theorems of Witten, J. Amer. Math. Soc. 2 (1989) 137 MR954493
5 G E Bredon, Representations at fixed points of smooth actions of compact groups, Ann. of Math. 89 (1969) 515 MR246324
6 A Dessai, Rigidity theorems for Spin-manifolds, Topology 39 (2000) 239 MR1722036
7 J Ebert, If the universal cover of a manifold is spin, must it admit a finite cover which is spin?, MathOverflow answer (2020)
8 A L Edmonds, Orientability of fixed point sets, Proc. Amer. Math. Soc. 82 (1981) 120 MR603614
9 H Herrera, R Herrera, Â-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, J. Differential Geom. 61 (2002) 341 MR1979364
10 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, E20, Vieweg & Sohn (1992) MR1189136
11 F Hirzebruch, P Slodowy, Elliptic genera, involutions, and homogeneous spin manifolds, Geom. Dedicata 35 (1990) 309 MR1066570
12 P S Landweber, editor, Elliptic curves and modular forms in algebraic topology, 1326, Springer (1988) MR970278
13 H B Lawson Jr., M L Michelsohn, Spin geometry, 38, Princeton Univ. Press (1989) MR1031992
14 K Liu, On modular invariance and rigidity theorems, J. Differential Geom. 41 (1995) 343 MR1331972
15 C H Taubes, S1 actions and elliptic genera, Comm. Math. Phys. 122 (1989) 455 MR998662
16 M Wiemeler, S1-equivariant bordism, invariant metrics of positive scalar curvature, and rigidity of elliptic genera, J. Topol. Anal. 12 (2020) 1103 MR4146575
17 E Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987) 525 MR885560