Events

Title: Products of CW complexes
Speaker's homepage

It's been a couple of years since I've spoken about CW complexes in a Leeds seminar, so for the benefit of newcomers and with apologies to the old hands who've seen it all before, this talk will be about my result on products of CW complexes. CW complexes are "nice" spaces that are often seen as good spaces to focus on for algebraic topology, avoiding many point-set-theoretic "pathologies". However, the product (as topological spaces) of two CW complexes need not be a CW complex. After giving all the necessary definitions I will go through my characterisation of exactly when the product is a CW complex; this characterisation involves the uncountable cardinal $\mathfrak{b}$.

Title: Pillay’s Conjecture for groups definable in weakly o-minimal non-valuational structures
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Let $M$ be a weakly o-minimal non-valuational structure, and $N$ its canonical o-minimal extension (by Wencel). We prove that every group $G$ definable in $M$ is a dense subgroup of a group $K$ definable in $N$. As an application, we obtain that $G^{00}= G\cap K^{00}$, and establish Pillay's Conjecture in this setting: $G/G^{00}$, equipped with the logic topology, is a compact Lie group, and if G has finitely satisfiable generics, then $\dim(G/G^{00})= \dim(G)$.