Steenrod problem
From Manifold Atlas
Revision as of 12:18, 31 March 2011 by Haggai Tene (Talk | contribs)
This page has not been refereed. The information given here might be incomplete or provisional. |
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
Cite error:
<ref>
tags exist, but no <references/>
tag was found