#### 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