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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the linear independence of certain cohomology classes in the classifying space for subfoliations


Author: Demetrio Domínguez
Journal: Trans. Amer. Math. Soc. 329 (1992), 221-232
MSC: Primary 57R32; Secondary 57R20
DOI: https://doi.org/10.1090/S0002-9947-1992-1024769-0
MathSciNet review: 1024769
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Abstract: The purpose of this paper is to establish the linear independence of certain cohomology classes in the Haefliger classifying space $ B{\Gamma _{({q_1},{q_2})}}$ for sub-foliations of codimension $ ({q_{1,}}{q_2})$. The classes considered are of secondary type, not belonging to the subalgebra of $ H(B{\Gamma _{({q_1},{q_2})}},R)$ generated by the union of the universal characteristic classes for foliations of codimension $ {q_1}$ and $ {q_2}$ respectively, and are elements of the kernel of the canonical homomorphism $ H(B{\Gamma _{({q_1},{q_2})}},R) \to H(B{\Gamma _{{q_1}}} \times B{\Gamma _d},R)$ with $ d = {q_2} - {q_1} > 0$.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1024769-0
Article copyright: © Copyright 1992 American Mathematical Society

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