Comments on: Question for the audience http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/ Blogging ... up to homotopy. Wed, 07 Jan 2009 03:23:43 +0000 http://wordpress.org/?v=2.5 By: Matt http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-11 Matt Wed, 29 Aug 2007 23:32:35 +0000 http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-11 Hi Ben, If you are lucky, the Ext-algebra in question is 'intrinsically formal.' An algebra (A,m) is intrinsically formal if any minimal A-infinity structure (A,m_n) with m_2=m is isomorphic to (A,m) as an A-infinity algebra. A quick way to test this is to compute some Hochschild cohomology (I believe this is also originally due to Kadeishvili). See section 3 in this excellent <a href="http://front.math.ucdavis.edu/0310.5414" rel="nofollow">paper</a>. Hi Ben,
If you are lucky, the Ext-algebra in question is ‘intrinsically formal.’ An algebra (A,m) is intrinsically formal if any minimal A-infinity structure (A,m_n) with m_2=m is isomorphic to (A,m) as an A-infinity algebra. A quick way to test this is to compute some Hochschild cohomology (I believe this is also originally due to Kadeishvili). See section 3 in this excellent paper.

]]> By: The Infinite Seminar » Overview of the computation of A-infinity structures http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-9 The Infinite Seminar » Overview of the computation of A-infinity structures Wed, 29 Aug 2007 09:20:08 +0000 http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-9 [...] Webster asked, in a comment to the post Question for the audience for pointers to literature on the computation of A ∞-structures. Since I’m still out [...] […] Webster asked, in a comment to the post Question for the audience for pointers to literature on the computation of A ∞-structures. Since I’m still out […]

]]> By: Ben Webster http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-8 Ben Webster Tue, 28 Aug 2007 18:54:51 +0000 http://infinity.blogseminar.net/2007/08/23/question-for-the-audience/#comment-8 I think "black-box computation" sounds good. On a related note, I was wondering if you could point me to some references on the "usual methods" you mention above. I'm interested in the <math xmlns='http://www.w3.org/1998/Math/MathML' display='inline'><msub><mi>A</mi> <mn>∞</mn></msub></math>-structure on a particular Ext-algebra (for some coherent sheaves on a projective variety). In particular, I suspect said structure is formal, but am not really sure of how to go about proving it, and can't seem to find any good references. Any thoughts? I think “black-box computation” sounds good.

On a related note, I was wondering if you could point me to some references on the “usual methods” you mention above. I’m interested in the A ∞-structure on a particular Ext-algebra (for some coherent sheaves on a projective variety). In particular, I suspect said structure is formal, but am not really sure of how to go about proving it, and can’t seem to find any good references. Any thoughts?

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