Algebraic Topology I, Fall 2016

 

Instructor: Peter Teichner

Assistant: Daniel Kasprowski

Lectures: Mo/Wed 14:15 - 16:00, Wegelerstr. 10, Zeichensaal/Kleiner Hörsaal

Homework

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:

  1. Smooth manifolds and transversality

  2. Vector bundles and characteristic classes

  3. Thom isomorphism and intersection theory

  4. Cobordism groups and (stable) homotopy theory

  5. Rational Hurewicz theorem and rational bordism ring

  6. Hirzebruch’s signature theorem and exotic 7-spheres


References:

  1. John Milnor and James Stasheff, Characteristic Classes

  2. Morris Hirsch, Differential Topology


Related Material:

  1. Victor Guillemin and Alan Pollack, Differential Topology

  2. Martin Golubitsky and Victor Guillemin, Stable Mappings and their singularities

  3. Matthias Kreck, Differential Algebraic Topology

  4. Allen Hatcher, Algebraic Topology

  5. 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.