Grothendieck's Reconstruction Principle and 2-dimensional Topology and Geometry

Abstract

This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichmüller theory, the mapping class groups, $SL(2,\mathbf{C})$ representation variety of surface groups, and Thurston's theory of measured laminations.

27 pages, 11 figures. Communications in Contemporary Mathematics, to appear