The Bestvina–Feighn Combination Theorem became a standard tool in geometric group theory and has had many applications and generalizations (e.g.). Bestvina and Feighn also gave the first published treatment of Rips' theory of stable group actions on R-trees (the Rips machine) In particular their paper gives a proof of the Morgan–Shalen conjecture that a finitely generated group "G" admits a free isometric action on an R-tree if and only if "G" is a free product of surface groups, free groups and free abelian groups. A 1992 paper of Bestvina and Handel introduced the notion of a train track map for representing elements of Out("F""n"). In the same paper they introduced the notion of a "relative train track" and applied train track methods to solve the "Scott conjecture" which says that for every automorphism "α" of a finitely generated free group "Fn" the fixed subgroup of "α" is free of rank at most "n". Since then train tracks became a standard tool in the study of algebraic, geometric and dynamical properties of automorphisms of free groups and of subgroups of Out("Fn"). Examples of applications of train tracks include: a theorem of Brinkmann proving that for an automorphism "α" of "Fn" the mapping torus group of "α" is word-hyperbolic if and only if "α" has no periodic conjugacy classes; a theorem of Bridson and Groves that for every automorphism "α" of "Fn" the mapping torus group of "α" satisfies a quadratic isoperimetric inequality; a proof of algorithmic solvability of the conjugacy problem for free-by-cyclic groups; and others. Bestvina, Feighn and Handel later proved that the group Out("Fn") satisfies the Tits alternative, settling a long-standing open problem. In a 1997 paper Bestvina and Brady developed a version of discrete Morse theory for cubical complexes and applied it to study homological finiteness properties of subgroups of right-angled Artin groups. In particular, they constructed an example of a group which provides a counter-example to either the Whitehead asphericity conjecture or to the Eilenberg−Ganea conjecture, thus showing that at least one of these conjectures must be false. Brady subsequently used their Morse theory technique to construct the first example of a finitely presented subgroup of a word-hyperbolic group that is not itself word-hyperbolic.