Invariants from an analytic function on hyperbolic Dehn surgery space
type: Item
instance of: scholarly article
title: Invariants from an analytic function on hyperbolic Dehn surgery space
zbMATH Open document ID: 0897.57016
author: Mingqing Ouyang
published in: Mathematische Annalen
publication date: 1998-10-11T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/41927
review text: 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.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M50
zbMATH DE Number: 1031534
zbMATH Keywords: hyperbolic 3-manifold
zbMATH Keywords: ideal tetrahedrons
zbMATH Keywords: 3-manifold invariant
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
OpenAlex ID: W2134601087
DOI: 10.1007/S002080050036
Recommended article: A new invariant on hyperbolic Dehn surgery space
Recommended article: Analytic surgery and the eta invariant
Recommended article: Surgery formulae for analytical invariants of manifolds
Recommended article: On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
Recommended article: Gauge theoretic invariants of Dehn surgeries on knots
Recommended article: The shape of hyperbolic Dehn surgery space
Recommended article: Dehn surgery, homology and hyperbolic volume
Recommended article: Invariants of deformations of quotient surface singularities
Recommended article: Q4953598
Recommended article: Q4871235
description: scientific article; zbMATH DE number 1031534