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The Geometric Theory of the Fundamental Germ

Differential Geometry 2007-05-23 v2 Algebraic Topology

Abstract

The fundamental germ is a generalization of π1\pi_{1}, 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)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.

Keywords

Cite

@article{arxiv.math/0506275,
  title  = {The Geometric Theory of the Fundamental Germ},
  author = {T. M. Gendron},
  journal= {arXiv preprint arXiv:math/0506275},
  year   = {2007}
}

Comments

23 pages, 2 figures, submitted for publication