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