کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9497228 | 1630758 | 2005 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Quadratic functions on torsion groups
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We 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, and E. Looijenga and J. Wahl. Finally, we show that on this class of torsion groups, two quadratic functions q,qâ² are isomorphic if and only if they have equal associated Gauss sums and there is an isomorphism between the associated symmetric bilinear pairings bq and bqâ² which sends dq to dqâ², where dq is the homomorphism defined by dq(x)=q(x)-q(-x). This generalizes a classical result due to V. Nikulin. Our results are elementary in nature and motivated by low-dimensional topology.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 198, Issues 1â3, 1 June 2005, Pages 105-121
Journal: Journal of Pure and Applied Algebra - Volume 198, Issues 1â3, 1 June 2005, Pages 105-121
نویسندگان
Florian Deloup, Gwénaël Massuyeau,