Projective elliptic genera and elliptic pseudodifferential genera

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dc.contributor.authorHan, F.
dc.contributor.authorVarghese, M.
dc.date.issued2019
dc.description.abstractIn 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.
dc.description.statementofresponsibilityFei Han, Varghese Mathai
dc.identifier.citationAdvances in Mathematics, 2019; 358:106860-1-106860-25
dc.identifier.doi10.1016/j.aim.2019.106860
dc.identifier.issn1090-2082
dc.identifier.issn1090-2082
dc.identifier.orcidVarghese, M. [0000-0002-1100-3595]
dc.identifier.urihttp://hdl.handle.net/2440/122800
dc.language.isoen
dc.publisherElsevier
dc.relation.granthttp://purl.org/au-research/grants/arc/FL170100020
dc.rights©2019 Elsevier Inc.All rights reserved.
dc.source.urihttps://doi.org/10.1016/j.aim.2019.106860
dc.subjectProjective elliptic genera; projective elliptic pseudodifferential genera; graded twisted Chern character; modularity; schur functors
dc.titleProjective elliptic genera and elliptic pseudodifferential genera
dc.typeJournal article
pubs.publication-statusPublished

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