I am writing a proof where I need to keep tracks of pull back maps between cohomology groups. It happens that one of the pull backs is an isomorphism and its inverse appears often in the proof. Is there a good notation for this?
So far I have simply used $(f^*)^{-1}$, but this makes my formulas look quite messy and ugly. What cpuld I use instead?
In particular, would $f_*:=(f^*)^{-1}$ be a good notation?