Triangulations of 3-dimensional pseudomanifolds with an application to   state-sum invariants
  We demonstrate the triangulability of compact 3-dimensional topological pseudomanifolds and study the properties of such triangulations, including the Hauptvermutung and relations by Alexander star moves and Pachner bistellar moves. We also provide an application to state-sum invariants of 3-dimensional topological pseudomanifolds 
Markus Banagl, Greg Friedman