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Untwisting twisted spectral triples

Goffeng, Carl Henrik Tryggve Magnus LU ; Mesland, Bram and Rennie, Adam (2019) In International Journal of Mathematics 30(14).
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.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
twisted spectral triples, local index theory;, KK-theory, noncommutativegeometry
in
International Journal of Mathematics
volume
30
issue
14
article number
1950076
publisher
World Scientific Publishing
external identifiers
  • scopus:85074586452
ISSN
0129-167X
DOI
10.1142/S0129167X19500769
language
English
LU publication?
no
id
55d87666-c5d4-406c-85db-cc3419a33b6c
date added to LUP
2021-03-12 12:00:02
date last changed
2022-04-27 00:48:34
@article{55d87666-c5d4-406c-85db-cc3419a33b6c,
  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.}},
  author       = {{Goffeng, Carl Henrik Tryggve Magnus and Mesland, Bram and Rennie, Adam}},
  issn         = {{0129-167X}},
  keywords     = {{twisted spectral triples; local index theory;; KK-theory; noncommutativegeometry}},
  language     = {{eng}},
  number       = {{14}},
  publisher    = {{World Scientific Publishing}},
  series       = {{International Journal of Mathematics}},
  title        = {{Untwisting twisted spectral triples}},
  url          = {{http://dx.doi.org/10.1142/S0129167X19500769}},
  doi          = {{10.1142/S0129167X19500769}},
  volume       = {{30}},
  year         = {{2019}},
}