Lens spaces in the Regge calculus approach to quantum cosmology

We study the wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four-dimensional simplicial complex to be a cone over the boundary lens space, described by a single internal edge length, and a single boundary edge length, one can analyze in detail the analytic properties of the action in the space of complex edge lengths. The classical extrema and convergent steepest descent contours of integration yielding the wave function are found. Both the Hartle-Hawking- and Linde-Vilenkin-type proposals are examined and, in all cases, we find wave functions which predict a Lorentzian oscillatory behavior in the late universe. The behavior of the results under subdivision of the boundary universe is also presented.