Motive of the $SL_4$-character variety of torus knots

Angel González-Prieto; Vicente Muñoz

doi:10.1016/j.jalgebra.2022.06.008

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arXiv · 2006.01810

Motive of the $SL_4$-character variety of torus knots

Angel González-Prieto·Vicente Muñoz

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Abstract

In this paper, we compute the motive of the character variety of representations of the fundamental group of the complement of an arbitrary torus knot into $SL_4(k)$, for any algebraically closed field $k$ of zero characteristic. For that purpose, we introduce a stratification of the variety in terms of the type of a canonical filtration attached to any representation. This allows us to reduce the computation of the motive to a combinatorial problem.

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BibTeX RIS

Angel González-Prieto, Vicente Muñoz. 2022-05-14. Motive of the $SL_4$-character variety of torus knots. https://doi.org/10.1016/j.jalgebra.2022.06.008

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