Witten Genus and Elliptic Genera for Proper Actions
نویسندگان
چکیده
In this paper, we construct for the first time, Witten genus and elliptic genera on noncompact manifolds with a proper cocompact action by an almost connected Lie group prove vanishing rigidity results that generalise known compact actions manifolds. We also compute our some interesting examples, study non-spinc case in appendix.
منابع مشابه
The Truncated Witten Genus
In this paper we define and examine the truncated Witten genus. It is defined as the equivariant index of the Dirac operator on the manifold Map(Cp, M) with its natural Cp-action. Here, Map(Cp, M) is the space of maps from the cyclic group of order p into a closed, connected, spin manifold, By applying the Atiyah-Singer index theorem we give a topological formula for the truncated Witten genus ...
متن کاملLiouville Theory and Elliptic Genera
The structure and modular properties of N = 4 superconformal characters are reviewed and exploited, in an attempt to construct elliptic genera-like functions by decompactifying K3. The construction is tested against expressions obtained in the context of strings propagating in background ALE spaces of type AN−1, using the underlying superconformal theory N = 2 minimal ⊗ N = 2 Liouville.
متن کاملOrbifold Elliptic Genera and Rigidity
Let M be a closed almost complex manifold on which a compact connected Lie group G acts non-trivially. If the first Chern class of M is divisible by an integer N greater than 1, then its equivariant elliptic genus φ(M) of level N is rigid, i.e., it is constant as a virtual character of G. This result was predicted by Witten [W] and proved by Taubes [T], Bott-Taubes [BT] and Hirzebruch [H]. Elli...
متن کاملSpin-manifolds and elliptic genera
We present an extension of the “miraculous cancellation” formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. Relations to the Ochanine congruence formula on 8k + 4 dimensional Spinc manifolds are discussed. To cite this article: F. Han, W. Zhang, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 2003 Académie des sciences. Published b...
متن کاملEquivariant Elliptic Genera
We introduce the equivariant elliptic genus for open varieties and prove an equivariant version of the change of variable formula for blow-ups along complete intersections. In addition, we prove the equivariant elliptic genus analogue of the McKay correspondence for the ALE spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2021
ISSN: ['0010-3616', '1432-0916']
DOI: https://doi.org/10.1007/s00220-021-04269-7