TL;DR
This paper interprets the cyclic quantum dilogarithm as a cyclic 6j-symbol within the Weyl algebra framework and constructs a link invariant in 3-manifolds using modified 6j-symbols.
Contribution
It introduces a novel interpretation of the cyclic quantum dilogarithm as a 6j-symbol and develops a new invariant for links in 3-manifolds.
Findings
The cyclic quantum dilogarithm is identified as a cyclic 6j-symbol.
A new invariant of triangulated links in 3-manifolds is constructed.
The invariant is shown to be an ambient isotopy invariant.
Abstract
The cyclic quantum dilogarithm is interpreted as a cyclic 6j-symbol of the Weyl algebra, considered as a Borel subalgebra . Using modified 6j-symbols, an invariant of triangulated links in triangulated 3-manifolds is constructed. Apparently, it is an ambient isotopy invariant of links.
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