ICTS:29105

Video URL

Automorphisms of free groups of small rank, and their outer conjugacy classes - 3

Automorphisms of free groups of small rank, and their outer conjugacy classes - 3

(2024). Automorphisms of free groups of small rank, and their outer conjugacy classes - 3. SciVideos. https://youtube.com/live/E-7Rmo1VYaE

Automorphisms of free groups of small rank, and their outer conjugacy classes - 3. SciVideos, Jul. 31, 2024, https://youtube.com/live/E-7Rmo1VYaE 

          @misc{ scivideos_ICTS:29105,
            doi = {},
            url = {https://youtube.com/live/E-7Rmo1VYaE},
            author = {},
            keywords = {},
            language = {en},
            title = {Automorphisms of free groups of small rank, and their outer conjugacy classes - 3},
            publisher = {},
            year = {2024},
            month = {jul},
            note = {ICTS:29105 see, \url{https://scivideos.org/icts-tifr/29105}}
          }
François Dahmani (UGA, France) & Nicholas Touikan (UNB, Canada)
Talk numberICTS:29105
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

If G is a group, its outer-automorphism group Out(G) is obtained from Aut(G) by quotienting out inner automorphisms, that are conjugations by elements of G. It is natural to ask methods and invariants to discuss whether two elements of Out(G) are conjugate. Important examples are GLn(Z) as automorphism group of Zn, Mapping Class Groups as outer-automorphism groups of surface groups, and outer-automorphism groups of finitely generated free groups. The case of the free group of rank 2: Out(F2) is isomorphic to GL(2, Z) and the classification of its conjugacy classes is classical. In rank 3, it is well known that interesting features appear, and they illustrate the rich theory of train tracks, laminations, geometry of suspensions, and structure of the polynomially subgroups, associated to an automorphism. With Francaviglia, Martino, and Touikan, we produced a solution to the conjugacy problem in Out(F3), which is the aim of this mini-course.

References:

‘Introduction to group the...