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Journal Articles Michigan Mathematical Journal Year : 2014

Branched spherical CR structures on the complement of the figure-eight knot

Abstract

Abstract. We obtain a branched spherical CR structure on the com- plement of the figure-eight knot whose holonomy representation was given in [4]. There are essentially two boundary unipotent representations from the complement of the figure-eight knot into PU(2,1), which we call ρ1 and ρ2. We make explicit some fundamental differences between these two representations. For instance, seeing the figure-eight knot complement as a surface bundle over the circle, the behavior of the fundamental group of the fiber under the representa- tion is a key difference between ρ1 and ρ2.

Dates and versions

hal-01374789 , version 1 (01-10-2016)

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Elisha Falbel, Jieyan Wang. Branched spherical CR structures on the complement of the figure-eight knot. Michigan Mathematical Journal, 2014, 63, pp.635-667. ⟨10.1307/mmj/1409932636⟩. ⟨hal-01374789⟩
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