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Combinatorics of CAT(0) cubical complexes, crossing complexes and co-skeletons

Rowan Rowlands, University of Washington
Wednesday, May 24, 2023 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:
Rowan Rowlands
Rowan Rowlands


Given a polytopal complex \(X\), define its \(k\)th co-skeleton to be the collection of faces of dimension greater than \(k\), i.e. the complement of the \(k\)-skeleton. We study some topological aspects of co-skeletons, in particular deriving a long exact sequence that relates the homologies of co-skeletons to the homologies of links. We will apply these ideas to \(\mathrm{CAT}(0)\) cubical complexes, and conclude that a \(\mathrm{CAT}(0)\) cubical complex has some topological properties (e.g. Cohen–Macaulayness) if and only if a certain associated simplicial complex, the crossing complex, shares these properties.

Please take note of the earlier starting time: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–3:50. The main talk starts at 4:00.

Join Zoom Meeting:
Meeting ID: 915 4733 5974