Rigidity of Elliptic Genera: From Number Theory to Geometry and Back

Bringmann, Kathrin, Castro, Alexander Caviedes, Sabatini, Silvia and Schwagenscheidt, Markus . Rigidity of Elliptic Genera: From Number Theory to Geometry and Back. Int. Math. Res. Notices. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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DOI:10.1093/imrn/rnab172

Abstract

In this paper, we derive topological and number theoretical consequences of the rigidity of elliptic genera, which are special modular forms associated to compact almost complex manifolds. On the geometry side, we prove that rigidity implies relations between the Betti numbers and the index of a compact symplectic manifold admitting a Hamiltonian action of a circle with isolated fixed points. We investigate the case of maximal index and toric actions. On the number theoretical side, we prove that from each compact almost complex manifold of index greater than one, that can be endowed with the action of a circle with isolated fixed points, one can derive non-trivial relations among Eisenstein series. We give explicit formulas coming from the standard action on CPn.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Bringmann, Kathrin	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Castro, Alexander Caviedes	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Sabatini, Silvia	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Schwagenscheidt, Markus	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED