منابع مشابه
Exercises on characteristic classes
1. a) Compute the Stiefel-Whitney classes of the tangent bundle of RP . (Use the method from class for the tangent Chern classes of complex projectives spaces.) b) Conclude that if the tangent bundle is trivial, then n = 2 − 1 for some m. (In fact n must be 0, 1, 3, 7, but this is much harder to prove; one proof uses the Bott periodicity theorem.) c) Deduce (very easily!) a complete characteriz...
متن کاملCharacteristic Classes on Grassmann Manifolds
In this paper, we use characteristic classes of the canonical vector bundles and the Poincaré dualality to study the structure of the real homology and cohomology groups of oriented Grassmann manifold G(k, n). Show that for k = 2 or n ≤ 8, the cohomology groups H∗(G(k, n),R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poinc...
متن کاملOn Uniqueness of Characteristic Classes
We give tools to compare different maps from algebraic K-theory. The results apply in particular to group morphisms from K-theory to any suitable cohomology theory or to K-theory. In particular, we obtain a characterization of the Chern character and of the Adams operations on higher K-theory.
متن کاملA Note on Characteristic Classes
This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.
متن کاملCharacteristic 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...
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2014
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1302-54