LAUSR

Rank 1 character varieties of finitely presented groups

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1 Published in 2017 at "Geometriae Dedicata"

DOI: 10.1007/s10711-017-0281-6

Abstract: Let $$\mathfrak {X}(\Gamma ,G)$$X(Γ,G) be the G-character variety of $$\Gamma $$Γ where G is a rank 1 complex affine algebraic group and $$\Gamma $$Γ is a finitely presentable discrete group. We describe an algorithm, which… read more here.

Keywords: character varieties; finitely presented; rank character; varieties finitely ... See more keywords

Character varieties for real forms

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1 Published in 2019 at "Geometriae Dedicata"

DOI: 10.1007/s10711-019-00435-3

Abstract: Let $$\varGamma $$Γ be a finitely generated group and G a real form of $$\mathrm {SL}_n(\mathbb {C})$$SLn(C). We propose a definition for the G-character variety of $$\varGamma $$Γ as a subset of the $$\mathrm {SL}_n(\mathbb… read more here.

Keywords: character; mathrm mathbb; character varieties; mathbb ... See more keywords

INTERSECTION COHOMOLOGY OF RANK 2 CHARACTER VARIETIES OF SURFACE GROUPS

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0 Published in 2021 at "Journal of the Institute of Mathematics of Jussieu"

DOI: 10.1017/s1474748021000487

Abstract: For $G = \mathrm {GL}_2, \mathrm {SL}_2, \mathrm {PGL}_2$ we compute the intersection E-polynomials and the intersection Poincaré polynomials of the G-character variety of a compact Riemann surface C and of the moduli space of… read more here.

Keywords: intersection; character varieties; varieties surface; rank character ... See more keywords

Character varieties of odd classical pretzel knots

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0 Published in 2018 at "International Journal of Mathematics"

DOI: 10.1142/s0129167x1850060x

Abstract: We determine the [Formula: see text]-character variety for each odd classical pretzel knot [Formula: see text], and present a method for computing its A-polynomial. read more here.

Keywords: odd classical; classical pretzel; varieties odd; character varieties ... See more keywords

Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing

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1 Published in 2022 at "Symmetry"

DOI: 10.20944/preprints202204.0126.v1

Abstract: It is shown that the representation theory of some finitely presented groups thanks to their SL2(C) character variety is related to algebraic surfaces. We make use of the Enriques–Kodaira classification of algebraic surfaces and related… read more here.

Keywords: topology; character varieties; character variety; character ... See more keywords