  Neurodegeneration affects cortical gray matter leading to loss of cortical
mantle volume. As a result of such volume loss, the geometrical arrangement of
the regions on the cortical surface is expected to be altered in comparison to
healthy brains. Here we present a novel method to study the alterations in
brain cortical surface geometry in Parkinson's disease (PD) subjects with a
\emph{Geometry Networks (GN)} framework. The local geometrical arrangement of
the cortical surface is captured as the 3D coordinates of the centroids of
anatomically defined parcels on the surface. The inter-regional distance
between cortical patches is the signal of interest and is captured as a
geometry network. We study its topology by computing the dimensionality of
simplicial complexes induced on a filtration of binary undirected networks for
each geometry network. In a permutation statistics test, a statistically
significant ($p<0.05$) difference was observed in the homology features between
PD and healthy control groups highlighting its potential to differentiate
between the groups and their potential utility in disease diagnosis.
