Deformation theory studies families of mathematical objects that vary from a fixed object over a parameter space, especially infinitesimal families over rings with nilpotent elements. First-order deformations are commonly controlled by a tangent space, obstructions by a second cohomology group, and equivalences by infinitesimal automorphisms.
Deformation Theory
See also
Cohomology Group, Moduli Space, Tangent SpaceExplore with Wolfram|Alpha
References
Hartshorne, R. Deformation Theory. New York: Springer-Verlag, 2010.Cite this as:
Weisstein, Eric W. "Deformation Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DeformationTheory.html