Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Introduction to stable homotopy theory
Semester
WiSe 2021 / 22

Lecturer
Marc Hoyois

Type of course (Veranstaltungsart)
Seminar

German title
Einführung in die stabile Homotopietheorie

Contents

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.



Literature
  • 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


Recommended previous knowledge
Algebraic Topology II

Time/Date
Thursday 14-16

Location
TBA or online

Course homepage
http://www.mathematik.ur.de/hoyois/WS22/spectra/index.html
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • 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
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Modules
BSem, MV, MSem

ECTS
BSem und MSem: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16. LA-GySem:
6 LP. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16
+++ weitere Details: siehe Modulkatalog +++