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Metric Ricci Curvature and Flow for PL Manifolds

Emil Saucan (2013)

Actes des rencontres du CIRM

We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.

Minimality of toric arrangements

Giacomo d'Antonio, Emanuele Delucchi (2015)

Journal of the European Mathematical Society

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.

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