Research ArticleNo Access

The reduced Dijkgraaf–Witten invariant of double twist knots in the Bloch group of $𝔽_{p}$

Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

E-mail Address: karu@kurims.kyoto-u.ac.jp

https://doi.org/10.1142/S0218216521500553Cited by:0 (Source: Crossref)

Abstract

In 2004, Neumann showed that the complex hyperbolic volume of a hyperbolic 3-manifold $M$ can be obtained as the image of the Dijkgraaf–Witten invariant of $M$ by a certain 3-cocycle. After that, Zickert gave an analogue of Neumann’s work for free fields containing finite fields. The author formulated a geometric method to calculate a weaker version of Zickert’s analogue, called the reduced Dijkgraaf–Witten invariant, for finite fields and gave a formula for twist knot complements and $𝔽_{p}$ in his previous work. In this paper, we show concretely how to calculate the reduced Dijkgraaf–Witten invariants of double twist knot complements and $𝔽_{p}$ , and give a formula of them for $p = 7$ .

Keywords:

AMSC: 57K10, 57K31, 57K32

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