Fundamental Groups and Limits of Almost Homogeneous Spaces

Abstract: We show that for a sequence of proper length spaces $X_n$ with groups $\Gamma_n$ acting discretely and almost transitively by isometries, if they converge to a proper finite dimensional length space $X$, then $X$ is a nilpotent Lie group with an invariant sub-Finsler Carnot metric. Also, for large enough $n$, there are subgroups $\Lambda_n \leq \pi_1(X_n)$ and surjective morphisms $\Lambda_n\to \pi_1(X)$.

differential geometrymetric geometry

Audience: researchers in the topic

mms&convergence

Series comments: Join Zoom Meeting: cuaieed-unam.zoom.us/j/84506421108?pwd=cjM5Q3NZR2gyQnV3Sjdqci80RkVSUT09

Meeting ID: 845 0642 1108 Passcode: 182795