This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). This issue has been addressed previously, but here we present concrete counterexamples to claims in the literature that Fredholm modules can be obtained from these weaker variations of spectral triple. Our counterexamples are constructed using self-adjoint extensions of symmetric operators.
Additional Grant Number
Forsyth, I. G., Mesland, B. & Rennie, A. C. (2014). Dense domains, symmetric operators and spectral triples. New York Journal of Mathematics, 20 1001-1020.