A fundamental polyhedron for the figure-eight knot group

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

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HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Journal of High Energy Physics ◽

10.1007/jhep07(2012)131 ◽

2012 ◽

Vol 2012 (7) ◽

Cited By ~ 75

Author(s):

H. Itoyama ◽

A. Mironov ◽

A. Morozov ◽

And. Morozov

Keyword(s):

Figure Eight Knot

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Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds

Journal of Topology and Analysis ◽

10.1142/s1793525318500024 ◽

2017 ◽

Vol 10 (01) ◽

pp. 1-25

Author(s):

Stavros Garoufalidis ◽

Alan W. Reid

Keyword(s):

Discrete Spectrum ◽

Eisenstein Series ◽

Finite Volume ◽

Finite Covers ◽

Figure Eight Knot ◽

Complex Length

We construct infinitely many examples of pairs of isospectral but non-isometric [Formula: see text]-cusped hyperbolic [Formula: see text]-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada’s method in the cusped setting, and so in addition our pairs are finite covers of the same degree of a 1-cusped hyperbolic 3-orbifold (indeed manifold) and also have the same complex length spectra. Finally we prove that any finite volume hyperbolic 3-manifold isospectral to the figure-eight knot complement is homeomorphic to the figure-eight knot complement.

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