منابع مشابه
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...
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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...
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Let G be a topological group and let EC be a free contractible G-space. The Bore1 construction on a G-space X is the orbit space Xo = EC x G X. When asked what equivariant cohomology is, most people would answer Bore1 cohomology, namely H:(X) = H*(X,). This theory has the claim of priority and the merit of ready computability, and many very beautiful results have been proven with it. However, i...
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ژورنال
عنوان ژورنال: Journal of Homotopy and Related Structures
سال: 2014
ISSN: 2193-8407,1512-2891
DOI: 10.1007/s40062-013-0074-z