Lawton, S.Muñoz, Vicente2023-06-182023-06-1820160030-873010.2140/pjm.2016.282.173https://hdl.handle.net/20.500.14352/24505We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), 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 a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).spajournal articlehttp://msp.org/pjm/2016/282-1/pjm-v282-n1-p08-s.pdfhttp://msp.org/open access512.7Character varietyE-polynomialFree groupSL(3C)Geometria algebraica1201.01 Geometría Algebraica