2005/06/14 by T. M. Gendron, Gendron, T. M. · 1 citation
Mathematics · #14B0 #57R30 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #math.AT #math.DG #msc:14B0 #msc:57R30
paper · pdf · doi:10.48550/arxiv.math/0506275
23 pages, 2 figures, submitted for publication
arxiv created 2005/06/28 · arxiv updated 2009/12/01
The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions in math.DG/0506270. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mother germ is constructed, which is, unlike the fundamental germ, a topological invariant. The fundamental germs of the antenna lamination and the PSL(2,\Z) lamination are calculated, laminations for which the definition in math.DG/0506270 was not available. The mother germ is used to give a proof of a Nielsen theorem for the algebraic universal cover of a closed surface of hyperbolic type.