Untwisting twisted spectral triples
K-Theory and Homology
2020-07-21 v2 Operator Algebras
Quantum Algebra
Abstract
We examine the index data associated to twisted spectral triples and higher order spectral triples. In particular, we show that a Lipschitz regular twisted spectral triple can always be `logarithmically dampened' through functional calculus, to obtain an ordinary (i.e. untwisted) spectral triple. The same procedure turns higher order spectral triples into spectral triples. We provide examples of highly regular twisted spectral triples with nontrivial index data for which Moscovici's ansatz for a twisted local index formula is identically zero.
Keywords
Cite
@article{arxiv.1903.02463,
title = {Untwisting twisted spectral triples},
author = {Magnus Goffeng and Bram Mesland and Adam Rennie},
journal= {arXiv preprint arXiv:1903.02463},
year = {2020}
}
Comments
57 pages, full proof of meromorphic extensions added in this version