2023/05/27 by Tu, Loring W.
#14C17 #55N25 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary: 55R10 #Secondary 14M17
paper · doi:10.48550/arxiv.2305.17509
Under Poincaré duality, a smooth map of compact oriented manifolds induces a pushforward map in cohomology, called the "Gysin map." It plays an important role in enumerative geometry. Using the equivariant localization formula, the author gave in 2017 a general formula for the Gysin map of a fiber bundle with equivariantly formal fibers. Equivariantly formal manifolds include all manifolds with cohomology in only even degrees such as complex projective spaces, Grassmannians, and flag manifolds as well as G/H, where G is a compact Lie group and H is a closed subgroup of maximal rank. This article is a simplified exposition using the example of a projective bundle to illustrate the algorithm.