Photon-mediated non-Markovian dynamics in topological Riemannian nanospheres of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mi>B</mml:mi> <mml:msub> <mml:mi>i</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mm

Considering the interaction of a photon in the vicinity of a Riemannian nanomanifold of the topological insulator Bi2Se3, we report evidence of a non-Markovian measurement in terms of a cross-correlation between the measured spectrum and a simulated Markovian spectrum in the region of spectroscopic optics. The non-Markovian dynamics starting from the transverse absorption spectrum and the dielectric function is quantified, by solving the integro-differential equation associated with the memory kernel followed by a Laplace transform that expresses the dynamics in terms of the temperature and radius of the Riemann manifold. This approach allowed us to study the information flow between the quantum system and the quantification environment (nanosphere), without resorting to tracing distances between the two states of the open quantum system. Based on our observations, we theorise that torsion, curvature, and intrinsic properties in an n-manifold from the point of view of differential geometry are likely to influence the memory effects of topological open quantum systems in the second or third dimension, paving the way for further theoretical and experimental advancements.