Vol. 297, No. 2, 2018

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Combinatorial classification of quantum lens spaces

Peter Lunding Jensen, Frederik Ravn Klausen and Peter M. R. Rasmussen

Vol. 297 (2018), No. 2, 339–365
Abstract

We answer the question of how large the dimension of a quantum lens space must be, compared to the primary parameter $r$, for the isomorphism class to depend on the secondary parameters. Since classification results in ${C}^{\ast }$-algebra theory reduce this question to one concerning a certain kind of $SL$-equivalence of integer matrices of a special form, our approach is entirely combinatorial and based on the counting of certain paths in the graphs shown by Hong and Szymański to describe the quantum lens spaces.

Keywords
quantum lens space, C*-algebra, SL equivalence
Primary: 46L35
Secondary: 05C30