Invariants from an analytic function on hyperbolic Dehn surgery space
Let \(M\) be a complete finite volume hyperbolic 3-manifold having cusps with an ideal triangulation, obtained as a union of ideal tetrahedrons in \(\mathbb H^3\). From the triangulation of \(M\), one can obtain \(K_\Delta (M)\), the field over \(\mathbb Q\), generated by tetrahedral parameters as an invariant. In this paper, the author shows that a sequence of subfields of \(K_\Delta (M)\) forms invariants of \(M\), and these contain information about how \(M\) is glued up. These invariants are extracted from an analytic function on the hyperbolic Dehn surgery space. Such a function is related to the variation of the cusps as the hyperbolic structure on \(M\) is deformed. It is also shown that the coefficients of the Taylor series expansion of this analytic function coincide with the coefficients of another one when the functions are associated with a pair of mutant hyperbolic knots.
scientific article; zbMATH DE number 1031534