UNTWISTING SPECTRAL TRIPLES

Connes and Moscovici introduced twisted spectral triples over a decade ago as a way of extending spectral noncommutative geometry of finite spectral dimension to situations where no finitely summable spectral triples exist. While there are attractive examples where twisted spectral triples provide a natural noncommutative geometry, one might ask for structural results relating twisted and untwisted spectral triples. In this talk, we discuss how the logarithm provides a way to untwist twisted spectral triples. This way we transform finitely summable twisted spectral triples to ordinary theta-summable spectral triples. By examples, we show the preservation of difficulty when it comes to index theory.