Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Yuji Tachikawa, 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 $pi_dmathrmTMF$
with spin manifolds whose boundaries are equipped with string structure. A few
negative-degree elements of $pi_dmathrmTMF$ 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 $pi_dmathrmTMF$,
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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