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arXiv · 1803.06144

Homotopy invariants of singularity categories

Sira Gratz·Greg Stevenson
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Abstract

We present a method for computing $\mathbb{A}^1$-homotopy invariants of singularity categories of rings admitting suitable gradings. Using this we describe any such invariant, e.g. homotopy K-theory, for the stable categories of self-injective algebras admitting a connected grading. A remark is also made concerning the vanishing of all such invariants for cluster categories of type $A_{2n}$ quivers.

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Sira Gratz, Greg Stevenson. 2018-03-16. Homotopy invariants of singularity categories. https://arxiv.org/abs/1803.06144

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