On pg125 on proving that that the concordance classes quotiented by the acyclic ones froms a group, there is a lemma:
Lemma 8.4.5 Let $(E,F,f)$ and $(E,F,g)$ be two $K$-cycles on $(X,Y)$. Assume that $$f^*g +g^*f \ge 0 \text{ or } fg^*+gf^* \ge 0$$ holds over $Y$. Then these two cycles are homotopic.
I do not understand this statement, where does the equality come from? At best I know locally we can regard the bundle morphism $f$ as a map $f:U \rightarrow GL_n(\Bbb C)$.
What is $f^*$? Is it the conjugate?