In 2012 Ananthnarayan, Avramov and Moore defined a connected sum of two Gorenstein local rings as an appropriate quotient of their fiber product. This new construction of connected sums always produces a Gorenstein ring.
In this talk, we discuss connected sums R#S of Gorenstein Artin local rings R and S over their common residue field k. We first investigate conditions that force Gorenstein Artin local rings to be indecomposable as connected sums. We also give a characterization for Gorenstein Artin local rings to be decomposable as connected sums. Furthermore, we show that the indecomposable components appearing in the connected sum decomposition are unique up to isomorphism.
This presentation is based on a recent joint work with H. Ananthnarayan, Jai Laxmi, and Z. Yang. Speaker(s): Ela Celikbas (West Virginia University)