Subject: (for the alg-top list ) A_infty structures and Hochschild cohomology Date: Wed, 06 Mar 2002 16:57:31 -0500 From: "John R. Klein" Can someone help me out here? Hochschild cohomology seems to come up in two ways in the theory of A_infty structures: First way: As the target recepticle for the obstructions to going from A_n-structures to A_{n+1}-structures (relative to a fixed A_{n-1}-structure). I'm thinking here about the work of Alan Robinson. Second way: In Gerstenhaber deformation theory of rings, the Hochschild cohomology codifies the infinitesimal deformations of associative structures on rings. Also, my understanding is that the "newer" deformation theory for A_infty algebra structures also has obstructions living in Hochschild cohomology groups. My Question: What relationship is there (if any) between the first way and the second way? That is, what's the connection between Robinson's work and deformation theory? John Klein