We give a simple geometric argument to derive in a common manner orthospectrum identities of Basmajian and Bridgeman. Our method also considerably simplifies the determination of the summands in these identities. For example, for every odd integer , there is a rational function of degree so that if is a compact hyperbolic manifold of dimension with totally geodesic boundary , there is an identity where the sum is taken over the orthospectrum of . When , this has the explicit form .
"Chimneys, leopard spots and the identities of Basmajian and Bridgeman." Algebr. Geom. Topol. 10 (3) 1857 - 1863, 2010. https://doi.org/10.2140/agt.2010.10.1857