Genres elliptiques équivariants. (Equivariant elliptic genera). (French) Zbl 0649.57023
Elliptic curves and modular forms in algebraic topology, Proc. Conf., Princeton/NJ 1986, Lect. Notes Math. 1326, 107-122 (1988).
[For the entire collection see Zbl 0642.00007.]
This paper describes the general process by which a genus in the sense of Hirzebruch leads to an equivarint genus for manifolds with G action. Using this process, the paper describes Witten’s conjecture, and gives a proof for the special case of semi-free actions. Specifically, it is shown that if \(\Phi\) is an elliptic genus and M is a Spin manifold with semifree circle action, then the equivariant genus \(\Phi_ s(M)\) is constant.
This paper describes the general process by which a genus in the sense of Hirzebruch leads to an equivarint genus for manifolds with G action. Using this process, the paper describes Witten’s conjecture, and gives a proof for the special case of semi-free actions. Specifically, it is shown that if \(\Phi\) is an elliptic genus and M is a Spin manifold with semifree circle action, then the equivariant genus \(\Phi_ s(M)\) is constant.
Reviewer: R.E.Stong
MSC:
| 57R20 | Characteristic classes and numbers in differential topology |
| 57S15 | Compact Lie groups of differentiable transformations |
| 58J20 | Index theory and related fixed-point theorems on manifolds |
| 14C35 | Applications of methods of algebraic \(K\)-theory in algebraic geometry |
| 11F11 | Holomorphic modular forms of integral weight |
| 58J26 | Elliptic genera |
