Another important contribution by Culler came in a 1986 paper with Karen Vogtmann called "Moduli of graphs and automorphisms of free groups".[4] This paper introduced an object that came to be known as Culler–Vogtmann Outer space.
Culler is one of the authors of a 1994 paper called "Plane curves associated to character varieties of 3-manifolds"[5] which introduced the A-polynomial of a knot[6] or, more generally, of a 3-manifold with one torus boundary component.
Culler, Marc; Shalen, Peter B.; Varieties of group representations and splittings of 3-manifolds.Annals of Mathematics. (2) 117 (1983), no. 1, 109–146.
Culler, Marc; Gordon, C. McA.; Luecke, J.; Shalen, Peter B. Dehn surgery on knots. Annals of Mathematics (2) 125 (1987), no. 2, 237–300.
Marc Culler and Karen Vogtmann; A group-theoretic criterion for property A. Proc. Amer. Math. Soc., 124(3):677—683, 1996. MR1307506
^D. Cooper, M. Culler, H. Gillet, D. D. Long and P. B. Shalen. Plane curves associated to character varieties of 3-manifolds. Invent. Math., 118(1):47--84, 1994.