Orbifold equivalence: structure and new examples

Journal of Singularities
volume 17 (2018), 216-244

Received: 10 October 2017. Received in revised form: 1 June 2018

DOI: 10.5427/jsing.2018.17j

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Abstract:

Orbifold equivalence is a notion of symmetry that does not rely on group actions. Among other applications, it leads to surprising connections between hitherto unrelated singularities. While the concept can be defined in a very general category-theoretic language, we focus on the most explicit setting in terms of matrix factorisations, where orbifold equivalences arise from defects with special properties. Examples are relatively difficult to construct, but we uncover some structural features that guarantee that certain perturbation expansions (which a priori are formal power series) are actually finite. We exploit those properties to devise a search algorithm that can be implemented on a computer, then present some new examples including Arnold singularities.

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