Affine lamination spaces for surfaces

Allen E. Hatcher and Ulrich Oertel

Vol. 154 (1992), No. 1, 87–101

DOI: 10.2140/pjm.1992.154.87

Abstract

In this paper we extend Thurston’s space 𝒫ℒ(M) of projective classes of measured laminations in the compact surface M to a space 𝒜ℒ(M) of laminations with transverse affine structures. The main theorem is that 𝒜ℒ(M) is homeomorphic to the product 𝒫ℒ(M) × H¹(M; ℝ).

Mathematical Subject Classification 2000

Primary: 57R30

Secondary: 57M50, 58F15

Milestones

Received: 15 November 1989

Published: 1 May 1992