Kavli Affiliate: Yuji Tachikawa
| Summary:
We construct and study a morphism of spectra implementing the Anderson duality of topological modular forms ($mathrmTMF$). Its differential version will then be introduced, allowing us to pair elements of $π_dmathrmTMF$ with spin manifolds whose boundaries are equipped with string structure. A few negative-degree elements of $π_dmathrmTMF$ will then be constructed using the theory of $mathrmRO(G)$-graded $mathrmTMF$, and will be identified using the differential pairing. We also discuss a conjecture relating vertex operator algebras and negative-degree elements of $π_dmathrmTMF$, underlying much of the discussions of this paper. The paper ends with a separate appendix for physicists, in which the contents of the paper are summarized and translated into their language.
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