Steenrod problem
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1 Introduction
Given a space X, there is a homomorphism , called the Thom homomorphism, given by where is the fundamental class of . The elements in the image of are called representable. In certain situations it is convenient to assume that a homology class is representable. In dimensions and it is clear that is surjective (even an isomorphism). It is less obvious in dimension , but also can be shown geometrically. This made Steenrod raise his famous problem in 1946 [1];: Given a simplicial complex , is every (integral) homology class representable?
2 References
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$ and \Phi : \Omega^{SO}_{∗}(X) \to H_{*}(X,\mathbb{Z}), called the Thom homomorphism, given by where is the fundamental class of . The elements in the image of are called representable.
In certain situations it is convenient to assume that a homology class is representable. In dimensions and it is clear that is surjective (even an isomorphism). It is less obvious in dimension , but also can be shown geometrically. This made Steenrod raise his famous problem in 1946 [1];:
Given a simplicial complex , is every (integral) homology class representable?
2 References
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$ it is clear that $\Phi$ is surjective (even an isomorphism). It is less obvious in dimension $, but also can be shown geometrically. This made Steenrod raise his famous problem in 1946 Insert footnote text here:
Given a simplicial complex $X$, is every (integral) homology class representable?
== References ==
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[[Category:Theory]]\Phi : \Omega^{SO}_{∗}(X) \to H_{*}(X,\mathbb{Z}), called the Thom homomorphism, given by where is the fundamental class of . The elements in the image of are called representable.
In certain situations it is convenient to assume that a homology class is representable. In dimensions and it is clear that is surjective (even an isomorphism). It is less obvious in dimension , but also can be shown geometrically. This made Steenrod raise his famous problem in 1946 [1];:
Given a simplicial complex , is every (integral) homology class representable?
2 References
Cite error:
<ref>
tags exist, but no <references/>
tag was found