We present a series of C^2-Morse functions on the Deligne-Mumford compactification M_{g,n} bar of the moduli space of genus g Riemann/hyperbolic surfaces with n punctures. This series of functions converges to the systole function, which is topologically Morse. We will show that the critical points of our functions approach those of systole sublinearly, stratum-wise, and with the same indices.PDF: C^2-Morse Functions on M_{g,n} bar.pdf
