MATH 7400 - Homological Algebra Fall 2013

Instructor: Yuri Berest

The course is intended to be an introduction to modern homological algebra. Topics will include abelian categories and classical derived functors (Ext and Tor); standard resolutions and (co)homology theories in algebra and geometry; derived and triangulated categories. Time permitting, we will give a brief introduction to Quillen’s theory of model categories and homotopical algebra.

References:

1. Gelfand and Yu. Manin, Methods of Homological Algebra, Springer, Berlin, 2000.
2. C. Weibel, An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, Cambridge, 1994.
3. J. Rotman, An Introduction to Homological Algebra, 2nd Edition, Springer, 2009.
4. J-L. Loday and B. Vallette, Algebraic Operads, Grundlehren der Mathematischen Wissenschaften 346, Springer, Heidelberg, 2012.
5. W. G. Dwyer and J. Spalinski, “Homotopy theories and model categories;” in Handbook of Algebraic Topology, Elsevier, 1995, pp. 73–126.