Gysin formulas and equivariant cohomology

Loring W. Tu

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arXiv · 2305.17509

Gysin formulas and equivariant cohomology

Loring W. Tu

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Abstract

Under Poincar\'e 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.

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BibTeX RIS

Loring W. Tu. 2023-05-27. Gysin formulas and equivariant cohomology. https://arxiv.org/abs/2305.17509

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