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Pensum til muntlig eksamen hentes fra
- Kapittel 1-7, 9 og 11
fra forelesningsnotatet spseq.pdf, men beviset for multiplikativitet av Serre-spektralsekvensen (i seksjon 6.4), bevisene i kapitlet om Steenrod-algebraen (kapittel 7), og bevisene for monoidal struktur i Adams-spektralsekvensen (seksjon 11.7-11.11) utelates.
Edvard Aksnes (edvardak@math.uio.no) er tillitsvalgt student.
The lectures will take place online, using Zoom. The passcode is 958021.
- Monday May 10 at 12.15-14.00
- Thursday May 20th at 12.15-14.00
- Thursday May 27th at 12.15-14.00
- Book format: Current notes
- Beamer presentation: Chapter 11
- Beamer presentation: Chapter 9
- Beamer presentation: Chapter 7
- Beamer presentation: Chapter 6
- Beamer presentation: Chapters 4 and 5
- Beamer presentation: Chapters 1, 2 and 3
The message Dokumenter contains links to my previous and current MAT9580 lecture notes, as well as to some articles and books referenced in the current notes.
- Adams: On the structure and applications of the Steenrod algebra
- Boardman: Conditionally convergent spectral sequences
- Cartan-Eilenberg: Homological Algebra
- Douady: La suite spectrale d’Adams : structure multiplicative
- Eilenberg-Steenrod: Foundations of Algebraic Topology
- Hatcher: Algebraic Topology
- Hatcher: Spectral Sequences
- Helle: Pairings and convergence of spectral sequences
- Mac Lane: Homology
- Mac Lane: Categories for the Working Mathematician
- Massey: Exact couples in algebraic topology (parts I and II)
- Massey: Exact couples in algebraic topology (parts III, IV and V)
- Massey: Products in exact couple...
I will lecture on the theory and applications of spectral sequences, with particular emphasis on the Adams spectral sequence calculating the stable homotopy groups of spheres.
- What is a spectral sequence?
- Convergence, exact couples
- Products, Cartan-Eilenberg systems
- Homological algebra, derived functors
- The stable homotopy category, orthogonal spectra
- The Adams spectral sequence
- The sphere spectrum
- Topological K-theory
- Bordism
- Topological modular forms