A generalization of Molino's theory and equivariant basic \^A-genus characters

Wenran Liu

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arXiv · 2105.07549

A generalization of Molino's theory and equivariant basic \^A-genus characters

Wenran Liu

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Abstract

Molino's theory is a mathematical tool for studying Riemannian foliations. In this paper, we propose a generalization of Molino's theory with two Riemannian foliations. For this purpose, the projection of foliation with respect to a fibration is discussed. The generalization results in an equivariant basic cohomological isomorphism in case of Killing foliation. It is a generalization of results given by Goertsches and T\"oben. We also give a geometric realization of the cohomological isomorphism through equivariant basic \^A-genus characters, who play a prominent role in calculating the index of an elliptic operator by Atiyah-Singer's index formula.

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Wenran Liu. 2021-05-17. A generalization of Molino's theory and equivariant basic \^A-genus characters. https://arxiv.org/abs/2105.07549

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