Chains on Peano continua, combinatorics and dynamics

Gianluca Basso, University of Turin

We generalize a theorem of Gutman, Tsankov and Zucker on the non-existence of generic chains of subcontinua in manifolds of dimension at least 3 to a large class of spaces. Among them is the Menger curve, a 1-dimensional planar continuum. Using Bing's partition theorem, we reduce the problem to a combinatorial statement about walks on finite graphs. The theorem has dynamical consequences which can be interpreted as non-rigidity results for the homeomorphism groups of the spaces involved. This is joint work with A. Codenotti and A. Vaccaro.

This seminar will be held both online and in person:

• Room: MC 5479
• Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09