Virginie Charette
Published 2003-11-04Version 1
Given an affine isometry of $\R^3$ with hyperbolic linear part, its Margulis invariant measures signed Lorentzian displacement along an invariant spacelike line. In order for a group generated by hyperbolic isometries to act properly on $\R^3$, the sign of the Margulis invariant must be constant over the group. We show that, in the case when the linear part is the fundamental group of a punctured torus, positivity of the Margulis invariant over any finite generating set does not imply that the group acts properly. This contrasts with the case of a pair of pants, where it suffices to check the sign of the Margulis invariant for a certain triple of generators.
Comments: 14 pages, 4 figures
On the fundamental group of semi-Riemannian manifolds with positive curvature operator
On polar foliations and fundamental group
Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
![QR code for arXiv:math/0311040 [math.DG]](http://oss.arxitics.com/images/favicon.svg)