Characteristic classes of homogeneous spaces

Characteristic Classes of Transversely Homogeneous Foliations

The foliations studied in this paper have transverse geometry modeled on a homogeneous space G/H with transition functions given by the left action of G. It is shown that the characteristic classes for such a foliation are determined by invariants of a certain flat bundle. This is used to prove that when G is semisimple, the characteristic classes are rigid under smooth deformations, extending ...

S^equivariant Function Spaces and Characteristic Classes

We determine the structure of the homology of the BeckerSchultz space SGiS1) ~ Q(CP^° AS1) of stable Sx-equivariant self-maps of spheres (with standard free S1 -action) as a Hopf algebra over the DyerLashof algebra. We use this to compute the homology of BSGiS1). Along the way, we give a fresh account of the partially framed transfer construction and the Becker-Schultz homotopy equivalence. We ...

Bundles, Classifying Spaces and Characteristic Classes

Introduction 1 1. Bundles 2 1.1. Pullback 2 1.2. Sections 3 1.3. Fiber bundles as fibrations 4 2. Vector bundles 4 2.1. Whitney sum 5 2.2. Sections of vector bundles 6 2.3. Inner products 6 3. Principal Bundles 7 3.1. Morphisms 7 3.2. Sections and trivializations 8 3.3. Associated bundles 9 3.4. Homotopy classification 11 3.5. B as a functor 14 4. Characteristic classes 16 4.1. Line Bundles 16 ...

Algebraic Homogeneous Spaces over Fields of Characteristic Two

Characteristic Classes

These are lecture notes for a series of five lectures I gave to other graduate students about characteristic classes through UT Austin’s summer minicourse program (see https://www.ma.utexas.edu/users/ richard.wong/Minicourses.html for more details). Beware of potential typos. In these notes I cover the basic theory of Stiefel-Whitney, Wu, Chern, Pontrjagin, and Euler classes, introducing some i...