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The Geometric Theory of the Fundamental Germ

Published online by Cambridge University Press:  11 January 2016

T. M. Gendron
T. M. Gendron*
Affiliation:
Instituto de Matemáticas - Unidad Cuernavaca, Universidad Nacional Autónoma de México, Av. Universidad s/n, C.P. 62210 Cuernavaca, Morelos, MÉXICO, [email protected]
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Abstract

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The fundamental germ is a generalization of π1, first defined for laminations which arise through group actions [4]. 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 [4] was not available. The mother germ is used to give a new proof of a Nielsen theorem for the algebraic universal cover of a closed surface of hyperbolic type.

Keywords

57R30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 190 , 2008 , pp. 1 - 34
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

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