## Elliptic genera in mathematics and physics and a generalization to G-manifolds

dc.rights.license | CC-BY-NC-ND | |

dc.contributor.advisor | Meier, F.L.M. | |

dc.contributor.author | Goertz, Leon | |

dc.date.accessioned | 2023-08-04T00:00:58Z | |

dc.date.available | 2023-08-04T00:00:58Z | |

dc.date.issued | 2023 | |

dc.identifier.uri | https://studenttheses.uu.nl/handle/20.500.12932/44484 | |

dc.description.abstract | Elliptic genera are a special type of manifold invariants that only depend on the bordism class of the manifolds. They can be constructed from elliptic curves and take values in modular forms. Important examples include the signature for 4n-manifolds and the so-called Â-genus which is related to the Dirac operator. A more general perspective is provided by complex genera which can be studied using formal group laws. This is the right setting for a generalization of elliptic genera to G-manifolds. For this, equivariant bordism and equivariant formal group laws are considered. In physics, elliptic genera arise as partition functions of supersymmetric string theories which has been originally described by Witten. Since then, this perspective has been further considered and gave rise to several developments in the mathematical theory. In this thesis, we will give an introduction to elliptic genera and compare the mathematical and physical perspective. Furthermore, we will explain their relations to formal group laws and outline the generalization of elliptic genera to the equivariant setting. | |

dc.description.sponsorship | Utrecht University | |

dc.language.iso | EN | |

dc.subject | I described the theory of elliptic genera in mathematics and physics from different perspectives. This includes their geometric construction from characteristic numbers, their properties as modular forms and relations to elliptic curves, their description using formal group laws, and their interpretation in string theory using index theory. Furthermore, I provided a definition of elliptic genera for G-manifolds using the theory of G-equivariant bordism G-equivariant formal group laws. | |

dc.title | Elliptic genera in mathematics and physics and a generalization to G-manifolds | |

dc.type.content | Master Thesis | |

dc.rights.accessrights | Open Access | |

dc.subject.keywords | elliptic genus; elliptic genera; bordism; manifold invariants; Pontryagin-Thom construction; modular forms; elliptic curves; formal group laws; equivariance; equivariant bordism; equivariant formal group laws; string theory; index of an elliptic operator; signature; Â-genus; tangential structure; DMVV-formula; orbifolds; orbifold elliptic genera; supersymmetry; partition function | |

dc.subject.courseuu | Mathematical Sciences | |

dc.thesis.id | 21037 |