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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We prove Poincar e Duality for L p cohomology, 1 p 1 We study the pairings between L p and L 1 and construct characteristic classes.
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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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Well known complexity classes such as NP, co-NP, P (PARITY-P), and PP are produced by considering a nondeterministic polynomial time Turing machine N and deening acceptance in terms of the number of accepting paths in N. That is, they are subclasses of P #PP1]. Other interesting classes such as MOD k P and C = P are also subclasses of P #PP1]. Many relations among these classes are unresolved. ...
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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...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.2307/1997617