The taut polynomial and the Alexander polynomial

Landry, Minsky and Taylor defined the taut polynomial of a veering triangulation. Its specialisations generalise Teichmuller fibred face Thurston norm ball. We prove that triangulation is equal to certain twisted Alexander underlying manifold. Then we give formulas relating untwisted polynomial. There are two formulas; one holds when maximal free abelian cover edge-orientable, another it not edge-orientable. Furthermore, consider 3-manifolds obtained by Dehn filling In this case formula relates specialisation under Dehn-filled This extends theorem McMullen connecting nonfibred setting, improves in case. also sufficient necessary condition for existence an orientable class cone over