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The sphere of spherical objects

Algebra & Discrete Mathematics

Speaker: Asilata Bapat, Australian National University
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Start time: Mon, May 2 2022, 11:00AM

Consider the 2-Calabi--Yau triangulated category arising from the zigzag algebra of the An quiver. The braid group acts on this category by twists in spherical objects. Given a Bridgeland stability condition, we describe how to realise the spherical objects as a dense subset of a piecewise-linear manifold. This manifold is canonically associated to the category, and the braid group acts on it piecewise-linearly. We also describe how the manifold transforms under wall-crossings of the stability condition. The talk is based on joint work with Anand Deopurkar and Anthony M. Licata.