On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
type: Item
instance of: scholarly article
title: On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
zbMATH Open document ID: 0829.58030
author: Marco Brunella
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1995-07-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73338
review text: The author constructs explicitly two surfaces of section for the geodesic flow \(\Phi^t\) on a compact hyperbolic surface \(\Sigma_g\) of genus \(g\geq 2\). These surfaces are diffeomorphic to a torus with \(4g+4\) (resp. \(4g+2\)) holes. The first return map of the geodesic flow on these surfaces of section can be related to the topological conjugacy class of the representation of \(\pi_1 (\Sigma_g)\) into the group of orientation preserving diffeomorphisms of the circle \(S^1\). This is used to show that the discrete Godbillon-Vey invariant for representations of \(\pi_1 (\Sigma_g)\) into the group of orientation preserving piecewise linear homeomorphisms \(h\) of \(S^1\) such that \(h' (x)\in \{\lambda^n\mid n\in \mathbb{Z}\}\) at every differentiable point \(x\in S^1\) and for some (fixed) \(\lambda>0\) is not invariant under topological conjugacy.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 778920
zbMATH Keywords: secondary invariants
zbMATH Keywords: hyperbolic surface
zbMATH Keywords: geodesic flow
zbMATH Keywords: topological conjugacy
MaRDI profile type: Publication
OpenAlex ID: W2324732866
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DOI: 10.5802/AFST.783
description: scientific article; zbMATH DE number 778920