The Geometric Theory of the Fundamental Germ

Details The Geometric Theory of the Fundamental Germ The Geometric Theory of the Fundamental Germ

2005-06-14

arxiv.org/abs/math/0506275v2

Mathematics

Differential Geometry

23 pages, 2 figures, submitted for publication

Scientific paper

The fundamental germ is a generalization of $\pi_{1}$, 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 $PSL(2,\Z)$ 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.

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