Representation Variety for the Rank One Affine Group

González-Prieto, Ángel; Logares, Marina; Muñoz, Vicente

doi:10.1007/978-3-030-84721-0_18

Cited by 2 publications

(2 citation statements)

References 36 publications

(56 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…recovering a result of González-Prieto, Logares, and Muñoz [15]. Alternatively, this result can also be obtained from the isomorphism of algebraic groups…”

Section: Upper Triangular 2 ×mentioning

confidence: 80%

See 1 more Smart Citation

Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

Hablicsek¹,

Vogel²

2022

SIGMA

View full text Add to dashboard Cite

In this paper, we use a geometric technique developed by González-Prieto, Logares, Muñoz, and Newstead to study the G-representation variety of surface groups X G (Σ g ) of arbitrary genus for G being the group of upper triangular matrices of fixed rank. Explicitly, we compute the virtual classes in the Grothendieck ring of varieties of the G-representation variety and the moduli space of G-representations of surface groups for G being the group of complex upper triangular matrices of rank 2, 3, and 4 via constructing a topological quantum field theory. Furthermore, we show that in the case of upper triangular matrices the character map from the moduli space of G-representations to the G-character variety is not an isomorphism.

show abstract

“…recovering a result of González-Prieto, Logares, and Muñoz [15]. Alternatively, this result can also be obtained from the isomorphism of algebraic groups…”

Section: Upper Triangular 2 ×mentioning

confidence: 80%

“…We remark that in an independent work [15], González-Prieto, Logares, and Muñoz computed the virtual class of the AGL 1 -representation varieties, where AGL 1 is the general affine group of the line. Their result can be deduced from our result on…”

Section: Resultsmentioning

confidence: 99%

Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

Hablicsek¹,

Vogel²

2022

SIGMA

View full text Add to dashboard Cite

show abstract

Pseudo-quotients of algebraic actions and their application to character varieties

Gonzalez-Prieto

2023

Commun. Contemp. Math.

View full text Add to dashboard Cite

In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good Geometric Invariant Theory (GIT) quotients regardless of their algebraic properties. The flexibility granted by their topological nature enables an easier identification in geometric constructions than classical GIT quotients. We obtain several results about the interplay between pseudo-quotients and good quotients. Additionally, we show that in characteristic zero pseudo-quotients are unique up to virtual class in the Grothendieck ring of algebraic varieties. As an application, we compute the virtual class of [Formula: see text]-character varieties for free groups and surface groups as well as their parabolic counterparts with punctures of Jordan type.

show abstract

Representation Variety for the Rank One Affine Group

Cited by 2 publications

References 36 publications

Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

Virtual Classes of Representation Varieties of Upper Triangular Matrices via Topological Quantum Field Theories

Pseudo-quotients of algebraic actions and their application to character varieties

Contact Info

Product

Resources

About