On the geometry of extensions of free groups
APA
(2024). On the geometry of extensions of free groups. SciVideos. https://youtube.com/live/gryt2RGJVco
MLA
On the geometry of extensions of free groups. SciVideos, Aug. 04, 2024, https://youtube.com/live/gryt2RGJVco
BibTex
@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}} }
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.