Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective elliptic genera and elliptic pseudodifferential genera   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.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin