TY - JOUR
T1 - Orbifold equivalence
T2 - Structure and new examples
AU - Recknagel, Andreas
AU - Weinreb, Paul
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85048705395&partnerID=8YFLogxK
U2 - 10.5427/jsing.2018.17j
DO - 10.5427/jsing.2018.17j
M3 - Article
AN - SCOPUS:85048705395
SN - 1949-2006
VL - 17
SP - 216
EP - 244
JO - Journal of Singularities
JF - Journal of Singularities
ER -