Algebraic Topology I, Fall 2016
Algebraic Topology I, Fall 2016
Instructor: Peter Teichner
Assistant: Daniel Kasprowski
Lectures: Mo/Wed 14:15 - 16:00, Wegelerstr. 10, Zeichensaal/Kleiner Hörsaal
Homework Sessions:
Mo. 8:15 - 10:00 in SemR 0.006, Julia Semikina
Fr. 10:15 - 12:00 in SemR 0.006, Felix Boes
Course Control Number: Masters Course V4D1
Prerequisites: Material equivalent to last year’s courses Topology 1+2, i.e.
CW-complexes, topological manifolds, homology, homotopy, cohomology, duality.
Content:
• Smooth manifolds and transversality
• Vector bundles and characteristic classes
• Thom isomorphism and intersection theory
• Cobordism groups and (stable) homotopy theory
• Rational Hurewicz theorem and rational bordism ring
• Hirzebruch’s signature theorem and exotic 7-spheres
References:
• John Milnor and James Stasheff, Characteristic Classes
• Morris Hirsch, Differential Topology
Related Material:
• Victor Guillemin and Alan Pollack, Differential Topology
• Martin Golubitsky and Victor Guillemin, Stable Mappings and their singularities
• Matthias Kreck, Differential Algebraic Topology
• Allen Hatcher, Algebraic Topology
• John Milnor, Topology from the Differential point of view (contains framed Pontrjagin-Thom construction)
Homework sheets will be posted online Wednesday evening HERE and are due in class on the following Wednesday.
Homework can only be submitted in groups of 2 or 3 students. We expect that these study groups meet regularly to discuss the homework and then each member writes up at least one problem.
To qualify for the final exam, your group has to collect at least 50% of the points awarded in the homework problems.
Final Exam:
15.2.2017, 9 - 11h, Wegelerstr. 10, Großer Hörsaal
To have a look at your graded exam, please come to Endenicher Allee, Room 3.022 on Wed., Feb. 22, 10 - 12h.
Second Exam:
20.3.2017, 9 - 11h, Wegelerstr. 10, Kleiner Hörsaal
You can have a look at your exam on Thursday, 10-11, in Daniel Kasprowski’s office.