15 citations · 17 across the 5 of their papers we have counts for
5 papers
Comparison of Levi-Civita connections in noncommutative geometry
Alexander Flamant, Bram Mesland, Adam Rennie
We compare the constructions of Levi-Civita connections for noncommutative algebras developed in arXiv:1505.07330, arXiv:1809.06721, arXiv:2403.13735. The assumptions in these vari…
Curvature and Weitzenbock formula for the Podleś quantum sphere
Bram Mesland, Adam Rennie
We prove that there is a unique Levi-Civita connection on the one-forms of the Dabrowski-Sitarz spectral triple for the Podleś sphere . We compute the full curvature ten…
Curvature and Weitzenbock formula for spectral triples
Bram Mesland, Adam Rennie
Using the Levi-Civita connection on the noncommutative differential one-forms of a spectral triple $(\B,\H,\D)$, we define the full Riemann curvature tensor, the Ricci curvature te…
Existence and uniqueness of the Levi-Civita connection on noncommutative differential forms
Bram Mesland, Adam Rennie
We combine Hilbert module and algebraic techniques to give necessary and sufficient conditions for the existence of an Hermitian torsion-free connection on the bimodule of differen…
Dense domains, symmetric operators and spectral triples
I. Forsyth, B. Mesland, A. Rennie
This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). We present counterexamples to claims in the literature…