A classification of special 2-fold coverings

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dc.creatorBauval, Anne
dc.creatorGoncalves, Daciberg L
dc.creatorHayat, Claude
dc.creatorMello, Maria Herminia de Paula Leite
dc.date2009-04-07
dc.date.accessioned2026-07-07T13:01:21Z
dc.date.available2026-07-07T13:01:21Z
dc.descriptionStarting with an O(2)-principal fibration over a closed oriented surface F_g, g>=1, a 2-fold covering of the total space is said to be special when the monodromy sends the fiber SO(2) = S^1 to the nontrivial element of Z_2. Adapting D Jonhson's method [Spin structures and quadratic forms on surfaces, J London Math Soc, 22 (1980) 365-373] we define an action of Sp(Z_2,2g), the group of symplectic isomorphisms of (H_1(F_g;Z_2),.), on the set of special 2-fold coverings which has two orbits, one with 2^{g-1}(2^g+1) elements and one with 2^{g-1}(2^g-1) elements. These two orbits are obtained by considering Arf-invariants and some congruence of the derived matrices coming from Fox Calculus. Sp(Z_2,2g) is described as the union of conjugacy classes of two subgroups, each of them fixing a special 2-fold covering. Generators of these two subgroups are made explicit.
dc.descriptionThis is the version published by Geometry & Topology Monographs on 29 April 2008
dc.identifierhttps://arxiv.org/abs/0904.1194
dc.identifierhttp://arxiv.org/abs/0904.1194
dc.identifierGeom. Topol. Monogr. 14 (2008) 27-47
dc.identifierdoi:10.2140/gtm.2008.14.27
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226121
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject57R15, 53C27
dc.titleA classification of special 2-fold coverings
dc.typetext

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