Realizing algebraic invariants of hyperbolic surfaces
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- by BoGwang Jeon PDF
- Trans. Amer. Math. Soc. 371 (2019), 147-172 Request permission
Abstract:
Let $S_g$ ($g\geq 2$) be a closed surface of genus $g$. Let $K$ be any real number field, and let $A$ be any quaternion algebra over $K$ such that $A\otimes _K\mathbb {R}\cong M_2(\mathbb {R})$. We show that there exists a hyperbolic structure on $S_g$ such that $K$ and $A$ arise as its invariant trace field and invariant quaternion algebra.References
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Additional Information
- BoGwang Jeon
- Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
- Address at time of publication: Department of Mathematics, POSTECH, 77 Cheong-Am Ro, Pohang, South Korea
- MR Author ID: 992711
- Email: bogwang.jeon@gmail.com
- Received by editor(s): January 6, 2016
- Received by editor(s) in revised form: September 11, 2016, and January 30, 2017
- Published electronically: July 12, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 147-172
- MSC (2010): Primary 11Z05, 57M99
- DOI: https://doi.org/10.1090/tran/7271
- MathSciNet review: 3885141