  The Gysin map of a map between compact oriented manifolds is the map in
cohomology induced by the push-forward map in homology. In enumerative
algebraic geometry, formulas for the Gysin map of a flag bundle play a vital
role. These formulas are usually proven by algebraic or combinatorial means.
This article shows how the localization formula in equivariant cohomology
provides a systematic method for calculating the Gysin homomorphism in the
ordinary cohomology of a fiber bundle. As examples, we recover classical
pushforward formulas for generalized flag bundles. Our method extends the
classical formulas to fiber bundles with equivariantly formal fibers.
