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.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01374789
Contributor : Elisha Falbel <>
Submitted on : Saturday, October 1, 2016 - 1:46:00 PM
Last modification on : Monday, June 3, 2019 - 9:20:02 AM

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  • HAL Id : hal-01374789, version 1

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

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