@article{ac51db1e06df4d18afa137e1b88f645a,
title = "Hyperbolic 3-manifolds and cluster algebras",
abstract = "We advocate the use of cluster algebras and their y-variables in the study of hyperbolic 3-manifolds. We study hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces, and show that cluster y-variables naturally give the solutions of the edgegluing conditions of ideal tetrahedra. We also comment on the completeness of hyperbolic structures.",
author = "Kentaro Nagao and Yuji Terashima and Masahito Yamazaki",
note = "Funding Information: Acknowledgments. K. N. is supported by the Grant-in-Aid for Research Activity Start-up (No. 22840023) and for Scientific Research (S) (No. 22224001). Y. T. is supported in part by the Grants-in-Aid for Scientific Research, JSPS (No. 22740036). M. Y. would like to thank PCTS and its anonymous donor for generous support. We would like to thank H. Fuji, A. Kato, S. Kojima, H. Masai, T. Nakanishi, S. Terashima, T. Yoshida and D. Xie for helpful conversation. Publisher Copyright: {\textcopyright} 2017 Foundation Nagoya Mathematical Journal.",
year = "2019",
month = sep,
day = "1",
doi = "10.1017/nmj.2017.39",
language = "English",
volume = "235",
pages = "1--25",
journal = "Nagoya Mathematical Journal",
issn = "0027-7630",
publisher = "Nagoya University",
}