Geometry and Topology Seminar

Keen's classical collar lemma quantifies the fact that, on a closed hy- perbolic surface, two intersecting geodesics cannot both have small length. Lee, Zhang, and independently Burger and Pozzetti recently proved striking generalizations of this collar lemma to certain surface group representations into higher rank Lie groups. In this talk I will present a new version of this collar lemma which holds in the unifying framework of positively ratioed representations, recently studied by Martone and Zhang. I will also discuss applications of this collar lemma to the study of degenerating sequences of representations.