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# Algebra Seminar

Date/Time/Room: Friday (11/30/2007) at 4:00pm in 487 Pickard Hall

Speaker: Mr. Frank Moore
Department of Mathematics
University of Nebraska-Lincoln

### "Cohomology of connected sums of artinian Gorenstein rings"

Abstract: Let $S$ and $T$ be artinian Gorenstein local rings with common residue field $k$. The connected sum $S \# T$ is the quotient of the fiber product $S \times_k T$ by the difference of the two socle elements; it is Gorenstein. We describe of the Koszul homology algebra $H(K^{S\#T}))$ in terms of the Koszul homology algebras of $S$ and $T$. In addition, we show that the quotient map $S \times_k T \longrightarrow S \# T$ is a Golod homomorphism. This provides information on the structure of the Ext algebra of $S \# T$, and hence a formula for the Poincar\'e series of $k$ over $S \# T$.

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