Christoph Schweigert. This topology course deals with singular homology and cohomology of topological spaces. On the level of cohomology we have the cup-product. This multiplicative structure together with the cap-product that combines cohomology and homology, is a further feature that allows us to use algebraic means in order to get geometric statements. This lecture aims at students in the master programs of mathematics, mathematical physics and physics.
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News Sheet no 10 has arrived! It contained a typo in exercise 2 thanks for making us aware. I screwed up the direction of the extension of A by B and correspondingly the domain of the boundary map was false. This is now corrected. The script is now finally available. Sorry for the delay. Nevertheless it is still very, very, very rough and all comments are welcome. Here it is. The exercise sessions are scheduled for tuesdays 10 am - 12 pm and thursday 10 am - 12 pm in room N 0.
There will be oral exams at the end of the semester. In the lecture we will cover the main modern computational tool in algebraic topology, namely spectral sequences.
We will particularly aim for the cohomology of fibre bundles and computations of homotopy groups of spheres. Along the way we will also develop the necessary theoretical background in homotopy theory and time permitting present the basics of stable homotopy theory. More specifically we plan to cover the following topics roughly in order : Spectral sequences in general Serre spectral sequence Some more foundational homotopy theory Computation of rational and low-dimensional homotopy groups of spheres Steenrod operations Complex K-Theory Atiyah-Hirzebruch spectral sequence Adams spectral sequence.
Sheet no 1 Sheet no 2 In exercise no 1, it should say rational cohomology! Adams: Stable Homotopy and generalised homology Ausoni: Algebraische Topologie II Kurzskript notes for a lecture course, available here , spectral sequences start around december 16th, in german Hatcher: Spectral sequences in algebraic topology unfinished project, available here McLeary: A user's guide to spectral sequences Switzer: Algebraich Topology - Homotopy and Homology Weibel: Homological Algebra News Catharina Stroppel und Prof.
Walter Purkert. Corona-Virus: Fachbibliothek Mathematik ab Das Mathematische Institut trauert um Dr. Antje Kiesel. Skip to the navigation. Skip to the content.
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Algebraic Topology II