Introduction to Stable Homotopy Theory

Stable homotopy theory is the study of spectra: homotopical versions of abelian groups. Long a part of algebraic topology proper, its techniques are now used across a range of neighbouring fields.

Topics

• the formalism of ∞-categories
• stable ∞-categories and the ∞-category of spectra
• May’s recognition principle for connective spectra
• homological algebra via derived ∞-categories
• examples and techniques: topological K-theory, localizations, completions

Schedule

Materials

• Stable Homotopy Theory and Higher Algebra (textbook in progress)

Exercises for this course are contained in the book.

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