Canonical components of character varieties of arithmetic two-bridge link complements
نویسندگان
چکیده
The desingularizations of the canonical components $$\textrm{SL}_2(\mathbb {C})$$ -character varieties arithmetic two-bridge link groups are determined.
منابع مشابه
Gonality and Genus of Canonical Components of Character Varieties
Throughout the paper,M will always denote a complete, orientable finite volume hyperbolic 3-manifold with cusps. By abuse of notation we will denote by ∂M to be the boundary of the compact manifold obtained from M by truncating the cusps. Given such a manifold, the SL2(C) character variety of M , X(M), is a complex algebraic set associated to representations of π1(M)→ SL2(C) (see §4 for more de...
متن کاملOn Character Varieties of Two-bridge Knot Groups
We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if t...
متن کاملHyperbolic Structures of Arithmetic Type on Some Link Complements
-d) u {00} c= CP = dH, and each a ePSL2(0d) determines an edge which is the geodesic in H having endpoints a//? and y/d. The tesselations 5^ and ^ are by regular ideal octahedra and tetrahedra, respectively, and are classical objects; for example, &\ is constructed in [2]. The tesselations «^, by ideal cuboctahedra, and ST-i, by ideal triangular prisms, are implicit in Chapter 6 of [9]; ^ is a ...
متن کاملArithmetic Harmonic Analysis on Character and Quiver Varieties
We propose a general conjecture for the mixed Hodge polynomial of the generic character varieties of representations of the fundamental group of a Riemann surface of genus g to GLn.C/ with fixed generic semisimple conjugacy classes at k punctures. This conjecture generalizes the Cauchy identity for Macdonald polynomials and is a common generalization of two formulas that we prove in this paper....
متن کاملCanonical Models of Arithmetic
In 1983 Takeuchi showed that up to conjugation there are exactly 4 arithmetic subgroups of PSL2(R) with signature (1;∞). Shinichi Mochizuki gave a purely geometric characterization of the corresponding arithmetic (1;∞)-curves, which also arise naturally in the context of his recent work on inter-universal Teichmüller theory. Using Bely̆ı maps, we explicitly determine the canonical models of thes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European journal of mathematics
سال: 2023
ISSN: ['2199-675X', '2199-6768']
DOI: https://doi.org/10.1007/s40879-023-00640-1