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Room P3.10, Mathematics Building
Björn Gohla, Grupo de Física Matemática, Universidade de Lisboa
Poincaré Duality as Duality of Categories
We give a construction that associates a small category $\mathcal{C}(X)$ to a CW-decomposition $X$ of a manifold. We obtain interesting families of finite categories from spheres and projective spaces as examples. Under some conditions this category $\mathcal{C}(X)$ seems to represent the homotopy type of $X$. Interestingly, for finite dimensional $X$ the Poincaré dual $\hat{X}$ has associated to it the opposite category $(\mathcal{C}(X))^{\rm{op}}=\mathcal{C}(\hat{X})$.
This is part of a joint project with Benjamin Heredia.
Please note the new date of 19th October - this seminar was originally scheduled for 12th October.