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

Autor:	Heusener, Michael, Munoz, Vicente, Porti, Joan
Rok vydání:	2015
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Geometry 14D20 57M25 57M27
Druh dokumentu:	Working Paper
Popis:	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). This 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 $Sym^2:SL(2,C) \to SL(3,C)$. 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. Comment: 30 pages, no figures. See http://mat.uab.cat/~porti/fig8.html for Mathematica notebooks and Sage worksheets associated to the computations in the paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1505.04451 Zobrazit plný text záznamu View this record from Arxiv