Connected sums of graded Artinian Gorenstein algebras and Lefschetz properties

Abstract In their paper [1] , H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A , B over a local Gorenstein ring T , which, in the graded Artinian case, can be viewed as an algebraic analogue of the topological construction of the same name. We give two alternative descriptions of this algebraic connected sum: the first uses algebraic analogues of Thom classes of vector bundles and Gysin homomorphisms , the second is in terms of Macaulay dual generators. We also investigate the extent to which the connected sum of A , B over an Artinian Gorenstein algebra T preserves the weak or strong Lefschetz property , thus providing new classes of rings which satisfy these properties.