Virtual classes of parabolic ${\mathrm{SL}}_2(\mathbb{C})$-character varieties

Abstract

In this paper, we compute the virtual classes in the Grothendieck ring of algebraic varieties of ${\mathrm{SL}}_2(\mathbb{C})$-character varieties over compact orientable surfaces with parabolic points of semi-simple type. When the parabolic punctures are chosen to be semi-simple non-generic, we show that a new interaction phenomenon appears generating a recursive pattern.

arXiv comment33 pages, 1 figure. Minor corrections added

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Cited by in corpus (7)

• A lax monoidal Topological Quantum Field Theory for representation varieties
• Motivic theory of representation varieties via Topological Quantum Field Theories
• Representation variety for the rank one affine group
• Motive of the $S{L}_4$-character variety of torus knots
• 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
• Virtual Classes of Character Stacks