Prof. D. Kotschick: Seminar on characteristic classes

• Time and place: The organisational meeting takes place on April 18th, at 2:15 PM in room B045.
  We will fix the time of the seminar then, the time given so far in LSF may be changed depending on participants' preferences.
• Summary: We will study characteristic classes of real and complex vector bundles.
  
• Intended audience: Master students of mathematics and/or physics. The seminar is suitable as a continuation of my differential geometry course last semester, and as a complement to Riemannian Geometry.
• Prerequisites: A basic knowledge of smooth manifolds and algebraic topology.
• References:
  Talks will be based on:
  [MS] J.W. Milnor and J.D. Stasheff: Characteristic classes, Princeton University Press
  Another useful reference is:
  [H] A. Hatcher: Vector Bundles and K-Theory
  
• List of talks:
  1 N.N.: Introduction to vector bundles ([MS] sect. 2 and 3, pp. 13--35; see also [H] sect. 1.1)
  2 N.N.: Axioms for Stiefel-Whitney classes and applications ([MS] sect. 4, pp. 37--54)
  3 N.N.: Grassmann manifolds and universal bundles ([MS] sect. 5, pp. 55--70; see also [H] sect. 1.2)
  4 N.N.: Cell structures for Grassmannians and the cohomology ring ([MS] sect. 6 and 7, pp. 73--87; see also [H] sect. 1.2 and 3.1)
  5 N.N.: Existence of Stiefel--Whitney classes, and the Euler class ([MS] sect. 8 and 9, pp. 89--102; see also [H] sect. 3.1)
  6 N.N.: Thom isomorphism ([MS] sect. 10, pp. 105--114)
  7 N.N.: Computations on smooth manifolds ([MS] sect. 11, pp. 115--135)
  8 N.N.: Obstructions; and complex vector bundles and complex manifolds ([MS] sect. 12 and 13, pp. 139--153; see also [H] sect. 3.3)
  9 N.N.: Chern classes ([MS] sect. 14, pp. 155--170; see also [H] sect. 3.1)
  10 N.N.: Pontryagin classes; Chern and Pontryagin numbers ([MS] sect. 15 and 16, pp. 173--195)
  11 N.N.: Oriented bordism and Thom spaces ([MS] sect. 17 and 18, pp. 199--217)
  12 N.N.: Signature theorem ([MS] sect. 19, pp. 219--229)
  
• Registration: You can register for the seminar by emailing me. Please include information about yourself, e.g. what degree you are studying for, and a choice of which talks you are interested in giving (a first and a second choice).
  There will be an organisational meeting during the first week of lectures. We will also fix the time of the seminar then, the time given so far in LSF may be changed depending on participants' preferences.