Classical bounded turning property states that any two points $x, y$ of a domain $\Omega$ can be joined by a continuum whose diameter does not exceed $C |x - y|$ for some constant $C$. We will consider higher-dimensional versions of this condition (introduced by Alestalo and Väisälä in the nineties) which can be phrased either in homological or homotopical manner. I will discuss an example of a domain for which the homological condition is satisfied and the homotopical is not and show the connection of these properties with the idea of John and uniform domains. The talk is based on the work in progress with P. Goldstein, C.-Y. Guo, P. Koskela and D. Nandi.

Meeting ID: 880 1298 8951 Passcode: 576018