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Introduction to stable homotopy theory SemesterSoSe 2023 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, the Atiyah–Hirzebruch and Adams spectral sequences, and the relationship between stable homotopy and bordism of smooth manifolds. 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 I and II (in particular: homology groups, homotopy groups, CW complexes, Eilenberg–Mac Lane spaces) Time/Date Mi 16-17:30 Location M009 Course homepage https://hoyois.app.uni-regensburg.de/SS23/spectra/index.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
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 +++ |