By S. Zaidman

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**Example text**

Let cpn - t K(Q, 2) be the classifying map of the generator of H2(cpn; Q). Then the pullback of i n+1 E H 2n+2(K(Q, 2); Q) by this map is O. n+1 K(Q, 2n + 1) is defined. Again by a spectral sequence argument, we see that the above map induces an isomorphism in the rational cohomology. Hence it gives the localization at 0 of cpn. It follows that k = 2, 2n + 1 otherwise. 26. It is known that the cohomology algebra of the classifying space BGL(n; q ~ BU(n) of n-dimensional complex vector bundles is a polynomial algebra generated by the Chern classes 1.

Here P and E denote polynomial algebra and exterior algebra respectively. a. generated by elements of V. In this case we always assume that the degrees of elements of V are the same unless otherwise stated. We write A(V)k to emphasize that the degrees are all equal to k. 30. a. A is called minimal if it is connected, free and d is decomposable; that is d(A+) where A+ = c A+ A+ EBk>oA(k). a. a. of B. 31. a. a. If there exist a finite dimensional vector space V and an isomorphism B~A®A(V)k as graded algebras such that dv E A(k+1) for any element v E V, then we call A c B a Hirsch extension or an elementary extension.

Ting values of integrals over them, we can decide whether a given closed form represents a rational cohomology class or not. However, this procedure cannot be considered as an intrinsic structure of the de Rham complex. Then there appeared the de Rham theory for simplicial complexes which turn out to be utilized to obtain information about their structure over Q. k = {(to,tI'''' ,tk) E JRk+l;ti 2 O,'L)i = l}. 49. (i) The restriction of any Coo differential form on JRHI to 6,k is called a Coo form on it.