Quadratic functions on torsion groups

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dc.creatorDeloup, Florian
dc.creatorMassuyeau, Gwenael
dc.date2003-01-06
dc.date2004-07-15
dc.date.accessioned2026-07-07T08:46:14Z
dc.date.available2026-07-07T08:46:14Z
dc.descriptionWe investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characteristic form, a quadratic function on a torsion group. When the associated symmetric bilinear pairing is fixed, we construct an affine embedding of a quotient of the set of characteristic forms into the set of all quadratic functions and determine explicitly its cokernel. We determine a suitable class of torsion groups so that quadratic functions defined on them are classified by the stable class of their lift. This refines results due to A.H. Durfee, V. Nikulin, C.T.C. Wall and E. Looijenga -- J. Wahl. Finally, we show that on this class of torsion groups, two quadratic functions are isomorphic if and only if they have equal associated Gauss sums and there is an isomorphism between the associated symmetric bilinear pairings which preserves the "homogeneity defects". This generalizes a classical result due to V. Nikulin. Our results are elementary in nature and motivated by low-dimensional topology.
dc.description15 pages; a few minor modifications (improved writing, lengthened abstract)
dc.identifierhttps://arxiv.org/abs/math/0301040
dc.identifierhttp://arxiv.org/abs/math/0301040
dc.identifierJ. Pure Applied Algebra 198:1-3 (2005) 105-121
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143184
dc.subjectCommutative Algebra
dc.subjectGeometric Topology
dc.subject15A63, 11E81, 11E39
dc.titleQuadratic functions on torsion groups
dc.typetext

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