Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/122800
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Type: | Journal article |
Title: | Projective elliptic genera and elliptic pseudodifferential genera |
Author: | Han, F. Varghese, M. |
Citation: | Advances in Mathematics, 2019; 358:106860-1-106860-25 |
Publisher: | Elsevier |
Issue Date: | 2019 |
ISSN: | 1090-2082 1090-2082 |
Statement of Responsibility: | Fei Han, Varghese Mathai |
Abstract: | In this paper, we construct for the first time the projective elliptic genera for a compact oriented manifold equipped with a projective complex vector bundle. Such projective elliptic genera are rational q-series that have topological definition and also have analytic interpretation via the fractional index theorem in Mathai-Melrose-Singer (2006) without requiring spin condition. We prove the modularity properties of these projective elliptic genera. As an application, we construct elliptic pseudodifferential genera for any elliptic pseudodifferential operator. This suggests the existence of putative rotation-equivariant elliptic pseudodifferential operators on loop space whose equivariant indices are elliptic pseudodifferential genera. |
Keywords: | Projective elliptic genera; projective elliptic pseudodifferential genera; graded twisted Chern character; modularity; schur functors |
Rights: | ©2019 Elsevier Inc.All rights reserved. |
DOI: | 10.1016/j.aim.2019.106860 |
Grant ID: | http://purl.org/au-research/grants/arc/FL170100020 |
Published version: | http://dx.doi.org/10.1016/j.aim.2019.106860 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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hdl_122800.pdf | Accepted version | 531.88 kB | Adobe PDF | View/Open |
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