Surgery Construction
Recall that in general, if are manifolds with boundary, then the boundary of the product manifold is .
Now, given a manifold of dimension and an embedding, define the -manifold
obtained by surgery, via cutting out the interior of and gluing in along their boundary . The trace of the surgery
defines an elementary cobordism . Note that is obtained from by surgery on . This is called reversing the surgery.
Every cobordism is a union of elementary cobordisms, by the work of Morse, Thom and Milnor.
Read more about this topic: Cobordism
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