Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T21:22:01.177Z Has data issue: false hasContentIssue false
  • English
  • Français

THE A-POLYNOMIAL HAS ONES IN THE CORNERS

Published online by Cambridge University Press:  01 March 1997

D. COOPER  and
D. D. LONG
D. COOPER
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
D. D. LONG
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
Get access

Abstract

1. Definition of the A-polynomial

The A-polynomial was introduced in [3] (see also [5]), and we present an alternative definition here. Let M be a compact 3-manifold with boundary a torus T. Pick a basis λ,μ of π1T, which we shall refer to as the longitude and meridian. Consider the subset RU of the affine algebraic variety R = Hom (π1M, SL2[Copf ]) having the property that ρ(λ) and ρ(μ) are upper triangular. This is an algebraic subset of R, since one just adds equations stating that the bottom-left entries in certain matrices are zero. There is a well-defined eigenvalue map

formula here

given by taking the top-left entries of ρ(λ) and ρ(μ).

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 231 - 238
Copyright
© The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)