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arXiv · 1405.0816

E-polynomial of the SL(3,C)-character variety of free groups

Sean Lawton·Vicente Muñoz
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Abstract

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3, C). Expanding upon existing techniques, we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give new proofs of the SL(2,C), PGL(2,C), and PGL(3,C) cases.

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Sean Lawton, Vicente Muñoz. 2014-05-05. E-polynomial of the SL(3,C)-character variety of free groups. https://doi.org/10.2140/pjm.2016.282.173

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