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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 112 NO.1 / (1996))
Finite coverings and surface fibrations
F. E. A. Johnson,
Pages. 41-52
Abstract The fundamental groups of closed 4-manifolds which fibre over a
hyperbolic surface, with fibre also a hyperbolic surface, constitute a natural
class of geometrical groups, herein denoted by $G^2$. Such groups are torsion
free and even satisfy Poincare' duality. We study their commensurablity classes
and establish criteria which enable us to rule out certain group extension from
membership of $G^2$. In consequence, we are able to show that $G^2$ is not
closed under of torsion-free extension by finite groups. At the geometrical
level, this leads to the construction of certain closed 4-manifolds which
whilst not themselves fibring in the desired manner, nevertheless, possess
finite coverings which do.
Contents 0. Introduction
1. Recollection of Fuchsian groups
2. A trichotomy on almost surface fibrations
3. Nonexistence criteria for surface fibrations
4. Construction of almost surface fibrations
Key words
Mathmatical Subject Classification