Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\eta$-invariant and Modular Forms   We show that the Atiyah-Patodi-Singer reduced $\eta$-invariant of the twisted
Dirac operator on a closed $4m-1$ dimensional spin manifold, with the twisted
bundle being the Witten bundle appearing in the theory of elliptic genus, is a
meromorphic modular form of weight $2m$ up to an integral $q$-series. We prove
this result by combining our construction of certain modular characteristic
forms associated to a generalized Witten bundle on spin$^c$-manifolds with a
deep topological theorem due to Hopkins.

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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph