Talk:Thom spaces (Ex)
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Revision as of 12:17, 2 April 2012 by Andreas Hermann (Talk | contribs)
Part 1
We define
and
where .
Part 2
If : is an embedding, we denote by : the composition of with the inclusion . In particular the normal bundles are related by . The bundle map induces
From the definition
we find for all
Part 3
Let the embeddings and be as in Part 2. Define the collapse maps
as in [Lück2001, page 57]. Then we have . For all we obtain
and
Part 4
Of course one can do similar things for non oriented manifolds or spin manifolds. One only has to modify the definition of and use the corresponding universal bundle instead of .