The SL(3, C)-character variety of the figure eight knot

Michael Heusener, Vicente Muńoz, Joan Porti

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

© 2017 University of Illinois. We give explicit equations that describe the character variety of the figure eight knot for the groups SL(3, C), GL(3, C) and PGL(3, C). For any of these G, it has five components of dimension 2, one consisting of totally reducible representations, another one consisting of partially reducible representations, and three components of irreducible representations. Of these, one is distinguished as it contains the curve of irreducible representations coming from SL(2, C). The other two components are induced by exceptional Dehn fillings of the figure eight knot. We also describe the action of the symmetry group of the figure eight knot on the character varieties.
Original languageEnglish
Pages (from-to)55-98
JournalIllinois Journal of Mathematics
Volume60
Issue number1
Publication statusPublished - 1 Jan 2016

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