This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.
Author(s): Martin Markl
Series: CBMS Regional Conference Series in Mathematics 116
Publisher: American Mathematical Society
Year: 2012
Language: English
Commentary: decrypted from 0471EA8D07DB85E8F31F0F29DFD7A42B source file
Pages: X+129
Cover
Title page
Contents
Preface
Basic notions
Deformations and cohomology
Finer structures of cohomology
The gauge group
The simplicial Maurer-Cartan space
Strongly homotopy Lie algebras
Homotopy invariance and quantization
Brief introduction to operads
?_{∞}-algebras governing deformations
Examples
Index
Bibliography
Back Cover
