Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
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