Mladen Bestvina

Mladen Bestvina (born 1959)[1] is a Croatian-American mathematician working in the area of geometric group theory.

John Walsh wrote in a review of Bestvina's monograph: 'This work, which formed the author's Ph.D. thesis at the University of Tennessee, represents a monumental step forward, having moved the status of the topological structure of higher-dimensional Menger compacta from one of "close to total ignorance" to one of "complete understanding".

A 1992 paper of Bestvina and Handel introduced the notion of a train track map for representing elements of Out(Fn).

[33] In the same paper they introduced the notion of a relative train track and applied train track methods to solve[33] 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).

Bestvina, Feighn and Handel later proved that the group Out(Fn) satisfies the Tits alternative,[37][38] settling a long-standing open problem.

In a 1997 paper[39] 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.