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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.

38 votes
6 answers
9k views

Deformation theory and differential graded Lie algebras

There is supposed to be a philosophy that, at least over a field of characteristic zero, every "deformation problem" is somehow "governed" or "controlled" by a differential graded Lie algebra. See for …
Kevin H. Lin's user avatar
14 votes
2 answers
2k views

"Spec" of graded rings?

From the discussion at Hochschild cohomology and A-infinity deformations, it seems that general Hochschild cohomology classes correspond to deformations where the deformation parameter can have nonzer …
Kevin H. Lin's user avatar
7 votes
3 answers
3k views

Hochschild cohomology and A-infinity deformations

When we are dealing with ordinary things or dg things (where thing = algebra or category), I think I understand how HH^2 corresponds to 1st order deformations and HH^3 corresponds to obstructions. On …
Kevin H. Lin's user avatar
39 votes
9 answers
5k views

What is a deformation of a category?

I have several naive and possibly stupid questions about deformations of categories. I hope that someone can at least point me to some appropriate references. What is a deformation of a (linear, dg, …
Kevin H. Lin's user avatar