Originally a subfield of algebraic topology that emerged in the second half of the 20th century, stable homotopy theory nowadays plays a much larger role in mathematics and has applications to various fields such as geometric topology, algebraic geometry, and even number theory.

The goal of this seminar is to introduce the central notion of spectrum and study its basic properties. Among other things, we will discuss the equivalence between spectra and generalized cohomology theories, the smash product of spectra, Spanier-Whitehead duality, Atiyah duality, the Steenrod algebra, and the Atiyah-Hirzebruch and Adams spectral sequences.

• J. F. Adams, Stable homotopy and generalised homology
• S. O. Kochman, Bordism, stable homotopy, and Adams spectral sequences
• R. M. Switzer, Algebraic Topology – Homotopy and Homology

• Organisational meeting/distribution of topics: Wednesday 14.07 at 16:15 in Zoom (meeting ID:
  685 9163 4224, passcode: adams), or by email at marc.hoyois@ur.de
• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk