E-polynomial of SL2(ℂ)-character varieties of free groups
2014 ◽
Vol 25
(06)
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pp. 1450058
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Keyword(s):
Let 𝖥r be a free group of rank r, 𝔽q a finite field of order q, and let SL n(𝔽q) act on Hom (𝖥r, SL n(𝔽q)) by conjugation. We describe a general algorithm to determine the cardinality of the set of orbits Hom (𝖥r, SL n(𝔽q))/ SL n(𝔽q). Our first main theorem is the implementation of this algorithm in the case n = 2. As an application, we determine the E-polynomial of the character variety Hom (𝖥r, SL 2(ℂ))// SL 2(ℂ), and of its smooth and singular locus. Thus we determine the Euler characteristic of these spaces.
2018 ◽
Vol 70
(2)
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pp. 354-399
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1949 ◽
Vol 1
(2)
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pp. 187-190
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1998 ◽
Vol 41
(2)
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pp. 325-332
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2019 ◽
Vol 12
(2)
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pp. 590-604
2015 ◽
Vol 159
(1)
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pp. 89-114
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Keyword(s):
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1981 ◽
Vol 24
(2)
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pp. 129-136
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Keyword(s):
2000 ◽
Vol 81
(2)
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pp. 257-284
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2006 ◽
Vol 16
(06)
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pp. 1031-1045
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