Homological Algebra

https://itmp.msu.ru/en/mscgeom...

A semester course introducing the basic constructions and techniques of homological algebra used in algebraic topology, algebraic geometry, and forming the basis of a number of geometric methods in mathematical physics.

The topics covered include chain complexes and differential graded al- gebras, quasi-isomorphisms, projective and injective modules, resolu- tions, homological dimension, Tor and Ext functors, regular sequences and Cohen–Macaulay rings, bicomplexes and filtered complexes, spec- tral sequences, A∞-morphisms.

Prerequisites: a basic course in algebra (groups, rings, modules, vector spaces), basic concepts of topology (continuous maps, homotopy).