Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds

We study invariants of 3-manifolds derived from finite abelian groups equip ped with quadratic forms. These invariants arise in Turaev's theory of modu lar categories and generalize those of H. Murakami, T. Ohtsuki and M. Okada . The crucial algebraic tool is a new reciprocity formula for Gauss sums, g eneralizing classical formulas of Cauchy, Kronecker, Krazer and Siegel. We use this reciprocity formula to give an explicit formula for the invariants and to generalize them to higher dimensions.