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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 ...

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
• ...

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