Updates on the Dehn paper

[Update June 28: A bit unrelated: Positive curvature and Bosons, which is one of the maybe more treacherous alleys in the saga of positive curvature. In any case, even if it could be a dead end, it is a passage not been walked before to link the known bosons for fundamental forces with the known even dimensional positive curvature manifolds. Still, the picture is a falsifiable scientific pursuit: it can be challenged by finding one single further positive curvature manifold beyond W24 or one single other Boson carrying forces. (The axion could be a candidate). This worked beautifully in Keplers Harmonices Mundi suggestion, where a single new planet killed the idea for good. What is nice that we do not only have a correspondence between Force bosons and even-dimensional positive curvature manifolds but also a correspondce between carriers with mass (gauge bosons and Higgs) and manifolds for which some Betti numbers are larger than 1. It is an epic conjecture of Ziller that all even-dimensional positive curvature manifolds have Betti numbers bounded above by 2.]

See also Chopping up Riemannian manifolds in the quantum calculus blog.
Here are some updates (mini blog) on A Dehn type invariant for Riemannian manifolds The first version of the ArXiv paper had contained mistakes and was updated corrections. Here is a local version [PDF] (last updated May 29, 2020) . The following chronological with the latest things on top as usual on blog rolls.