**Homological Methods in Noncommutative Geometry**

by D. Kaledin

2008**Number of pages**: 77

**Description**:

The first seven lectures deal with the homological part of the story (cyclic homology, its various definitions, various additional structures it possesses). Then there are four lectures centered around Hochschild cohomology and the formality theorem.

Download or read it online for free here:

**Download link**

(550KB, PDF)

## Similar books

**An informal introduction to the ideas and concepts of noncommutative geometry**

by

**Thierry Masson**-

**arXiv**

This is an extended version of a three hours lecture given at the 6th Peyresq meeting 'Integrable systems and quantum field theory'. We make an overview of some of the mathematical results which motivated the development of noncommutative geometry.

(

**6983**views)

**Surveys in Noncommutative Geometry**

by

**Nigel Higson, John Roe**-

**American Mathematical Society**

These lectures are intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, residue index theorem, etc.

(

**6818**views)

**Deformations of Algebras in Noncommutative Geometry**

by

**Travis Schedler**-

**arXiv**

In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as quantization of Poisson structures, and Kontsevich's formality theorem in the smooth setting.

(

**3593**views)

**Geometric Models for Noncommutative Algebra**

by

**Ana Cannas da Silva, Alan Weinstein**-

**University of California at Berkeley**

Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces.

(

**6712**views)