pl topology

First bullet point: There is an interesting analysis of the secret deals that led to the war in Ukraine at the moment by the New York Times, as well as an account of the Trump administration involvement.

This post is brought to you by the letter A for anger issues, and the failed attempt to find an HDMI cable. Why is it that usually there are enough of them to choke two species into extinction, rid Paris of her rat-issues and still have enough for the Praelatura Sanctae Crucis et Operis Dei to flagellate themselves biweekly, but now I cannot find a single one.

Second: Something is rotten in the state of Denmark. Ok, I am being overdramatic; though if I was talking about the level of paranoia this country sometimes presents when faced with youth whose skin is not piggy-pink, that could well be appropriate.

I am also not referring to royal family affairs and the queen’s dental care.

Also, the issue is not really restricted to Denmark. I just really wanted to quote Marcellus.

What I am referring to is an increasing effort to make university a school. And as someone who hated school, let me say:

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There is a surprising lack of intuition for PL manifolds around, which always surprised me. And it turns out you can answer some questions. We stay in the category of PL manifolds throughout. The following question was asked by Gil Kalai to Ed Swartz some 15 years ago. Ed could not answer the question, and popularized here.

Question (Kalai) Are there different (homeomorphism types of) triangulated closed compact homology $(d-1)$ -spheres $H$ with $g_3=0$ (for any $d$ )?

Without going too deep into what $g_3=0$ means, we note quite simply that it is equivalent to saying that $H$ is boundary to a triangulated manifold $D$ that has no interior simplices of dimension $d-3$ .