Abstract
The once-punctured torus and the once-punctured Klein bottle are topologically commensurable, in the sense that both of them are doubly covered by the twice-punctured torus. In this paper, we give a condition for a faithful type-preserving $\mathrm{PSL}(2,\mathbf{C})$-representation of the fundamental group of the once-punctured Klein bottle to be ‘‘commensurable’’ with that of the once-punctured torus. We also show that such a pair of $\mathrm{PSL}(2,\mathbf{C})$-representations extend to a representation of the fundamental group of a common quotient orbifold. Finally, we give an application to the study of the Ford domains.
Citation
Mikio Furokawa. "Commensurability between once-punctured torus groups and once-punctured Klein bottle groups." Hiroshima Math. J. 46 (2) 217 - 253, July 2016. https://doi.org/10.32917/hmj/1471024950
Information