Publication

Balanced Fiber Bundles and GKM Theory

Silvia Sabatini
2013
Journal Articles

Abstract

Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H-T*(B) as a subring of H-T*(B-T). In this paper, we prove an analog of this result for T-equivariant fiber bundles: we show that if M is a T-manifold and pi:M -> B a fiber bundle for which pi intertwines the two T-actions, there is a simple combinatorial description of H-T*(M) as a subring of H-T*(pi(-1)(B-T)). Using this result, we obtain fiber bundle analogs of results of Guillemin et al. [4] on GKM theory for homogeneous spaces.

Official source

https://infoscience.epfl.ch/entities/publication/9a7ef604-fe72-4293-beeb-7492d73adba3

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Silvia Sabatini
2013
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9a7ef604-fe72-4293-beeb-7492d73adba3

About this result

Related concepts (32)

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane.

Principal bundle

In mathematics, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product of a space with a group . In the same way as with the Cartesian product, a principal bundle is equipped with An action of on , analogous to for a product space. A projection onto . For a product space, this is just the projection onto the first factor, . Unlike a product space, principal bundles lack a preferred choice of identity cross-section; they have no preferred analog of .

Fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in Commonwealth English: fibre bundle) is a space that is a product space, but may have a different topological structure. Specifically, the similarity between a space and a product space is defined using a continuous surjective map, that in small regions of behaves just like a projection from corresponding regions of to The map called the projection or submersion of the bundle, is regarded as part of the structure of the bundle.

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Balanced Fiber Bundles and GKM Theory

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