ICTS:29128

Video URL

On the geometry of extensions of free groups

On the geometry of extensions of free groups

(2024). On the geometry of extensions of free groups. SciVideos. https://youtube.com/live/gryt2RGJVco

On the geometry of extensions of free groups. SciVideos, Aug. 04, 2024, https://youtube.com/live/gryt2RGJVco 

          @misc{ scivideos_ICTS:29128,
            doi = {},
            url = {https://youtube.com/live/gryt2RGJVco},
            author = {},
            keywords = {},
            language = {en},
            title = {On the geometry of extensions of free groups},
            publisher = {},
            year = {2024},
            month = {aug},
            note = {ICTS:29128 see, \url{https://scivideos.org/icts-tifr/29128}}
          }
Pritam Ghosh
Talk numberICTS:29128
Source RepositoryICTS-TIFR
Source EventGeometry in Groups
Collection

Abstract

Let F be a finite-rank free group with rank greater than 2, Q be a finitely generated subgroup of the outer automorphism group of F, and consider a short exact sequence
1 → F → EQ → Q → 1.
My talk will discuss some known results and some open questions regarding the geometry of EQ, given information about Q. There is a somewhat decent understanding of the geometry of EQ when Q is cyclic, where we have necessary and sufficient conditions on Q to determine if EQ is hyperbolic or relatively hyperbolic or thick. One key idea we will look into is – why EQ is relatively hyperbolic when Q is an infinite cyclic group generated by an exponentially growing outer automorphism of F and then discuss some difficulties one faces while extending such results to the cases when Q is not cyclic.