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The Geometric Theory of the Fundamental Germ

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arxiv math/0506275 v2 pith:5GTP3B3J submitted 2005-06-14 math.DG math.AT

classification math.DGmath.AT
keywords germfundamentallaminationlaminationsmathmotheractionsaddition
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abstract

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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  1. Primitive invariants from laminations

    math.GT 2025-07 reject novelty 3.0 of 10

    The paper proposes a lamination-based reformulation of Gromov-Witten invariants for complete intersections, but the main theorems are asserted without valid derivations.

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