Smoothings and controlled topology
Student No.:40
Time:Mon & Wed, 15:20-16:55
Instructor:Thomas Farrell  [Tsinghua University]
Place:Conference Room 3, Jin Chun Yuan West Bldg.
Starting Date:2018-3-5
Ending Date:2018-6-13

Abstract: The object of smoothing theory is to classify the distinct smooth structures on a topological manifold. It originated with the works of Milnor and Kervaire and was developed further by Cairns, Hirsch, Mazur and Munkres. And put into definitive form for manifolds of dimension not less than 5 by Kirby-Siebenmann and by Burghelea, Lashof and Rothenberg. Later Quinn found a relationship to metrically controlled topology. This course will expose these subjects and their relation to the study of the diffeomorphism group of a manifold.

Prerequisites: Elementary differential topology and basic fiber bundle theory.

Reference texts:
1. Milnor, Topology from a differentiable viewpoint.
2. Steenrod, The topology of fiber bundles
3. Kirby and Siebenmann, Foundational Essays on topological manifolds, smoothings and triangulations