Date, time, location
First half: Mon Aug 31 – Oct 12 13:15 – 15:00, room 3721, KTH.
Second half: Mon Nov 2 - Dec 14 13:15 - 15:00, room 306, SU.
Lecturers
First half: T. Bauer, KTH
Second half: G. Arone, SU
Course content
Homological algebra: rings and modules, chain complexes, homology, tensor products and homomorphism groups, projective and injective modules, categories and functors, resolutions, chain homotopies, Tor and Ext functors, group homology
Algebraic topology: singular homology, Eilenberg-Steenrod axioms, homology with coefficients, cohomology, universal coefficient theorem, cellular homology, cross product and cup product, cohomology rings, Künneth theorem
Prerequisites
Linear algebra, familiarity with the notions of groups and rings, topological spaces and basic point-set topology. Optimally, also familiarity with modules, the fundamental group, homotopies of maps.
Literature
- Charles A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, 1995
- a comprehensive and well-written book containing all of the homological algebra material of the lecture, and much more
- a comprehensive and well-written book containing all of the homological algebra material of the lecture, and much more
- Allen Hatcher, Algebraic topology, Cambridge University Press, 2001 (free online version)
- A good modern introduction to algebraic topology with the student in mind. Ideas are presented very well, details sometimes leave a bit to be desired.
- Glen E. Bredon, Topology and geometry, Springer Graduate Texts in Mathematics 139, 1997
- A classic text on algebraic topology from the viewpoint of geometry and manifold theory
- Tammo tom Dieck, Algebraic topology, EMS Textbooks in Mathematics, EMS Publishing House, 2010
- A modern, very careful and complete treatment of the fundamentals of algebraic topology. Somewhat encyclopedic in style; not to be read linearly.
- Wojciech Chachólski and Roy Skjelnes, Homological Algebra and Algebraic Topology, course notes from previous years
- This year's course will be a bit different in content and a lot different in the order we treat the material; still, these notes contain much of what we will do.
