Gysin map in complex cobordism ($f_{!}:M{U}^q(X)\to M{U}^{q+\dim Y-\dim X}(Y)$)

For a proper map with fixed complex normal orientation, apply the Thom isomorphism in complex cobordism, pull back by the collapse of a tubular neighborhood of a graph embedding, and desuspend the auxiliary Euclidean coordinates. The degree increase is the relative real codimension. Changing the orientation can change this map.