= Pinch map
{title2=$M\mathbin\#N\to M\vee N$}
A pinch map collapses a separating subspace to a point so that the quotient splits into a <wedge sum>. For a <connected sum of oriented manifolds>, collapsing the separating boundary sphere gives a map $M\mathbin\#N\to M\vee N$. The two wedge projections have <degree of a continuous mapping> one with compatible orientations. Consequently their pullbacks identify the two top <orientation classes>, while positive-degree classes from different summands have zero <cup product>.
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