Weight $1\mathrm{/}2$ multiplier systems for the group ${\mathrm{\Gamma }}_0^{+}(p)$ and a geometric formulation

We construct a weight $1\mathrm{/}2$ multiplier system for the group ${\mathrm{\Gamma }}_0^{+}(p)$, the normalizer of the congruence subgroup ${\mathrm{\Gamma }}_0(p)$ where $p$ is an odd prime, and we define an analogue of the eta function and Rademacher symbol and relate it to the geometry of edge paths in a triangulation of the upper half plane.