Titlebook: Volume Conjecture for Knots; Hitoshi Murakami,Yoshiyuki Yokota Book 2018 The Author(s), under exclusive licence to Springer Nature Singapo

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Hitoshi Murakami,Yoshiyuki Yokotah ist, wird die Richtung von . mit der von . übereinstimmen, d. h. es wird . = λ. sein, wo λ ein fester skalarer Faktor ist. Legen wir aber dem Punkt die Bedingung auf, in einer festen Ebene ε zu bleiben, so werden . und .im allgemeinen, d. h. wenn nicht auch . in . liegt, verschiedene Richtungen ha

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2197-1757 e and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the978-981-13-1149-9978-981-13-1150-5Series ISSN 2197-1757 Series E-ISSN 2197-1765

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,Idea of “Proof”,hird section, following Yokota (Interdiscip Inf Sci 9(1):11–21, 2003. MR MR2023102 (2004j:57014)) again, we explain the relationship between the hyperbolic structure of the knot complement, and a “potential” function which we obtain in the second section. In the fourth section, we sort the remaining

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2197-1757 etry of a knot complement.Gives the current status of the vo.The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrat

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