Geometric invariants for Seifert fibred 3-manifolds

Ouyang, Ming Qing

doi:10.1090/S0002-9947-1994-1257644-9

Geometric invariants for Seifert fibred $3$-manifolds
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by Ming Qing Ouyang PDF

Trans. Amer. Math. Soc. 346 (1994), 641-659 Request permission

Abstract:

In this paper, we obtain a formula for the $\eta$-invariant of the signature operator for some circle bundles over Riemannian $2$-orbifolds. We then apply it to Seifert fibred $3$-manifolds endowed with one of the six Seifert geometries. By using a relation between the Chern-Simons invariant and the $\eta$-invariant, we also derive some elementary formulae for the Chern-Simons invariant of these manifolds. As applications, we show that some families of these manifolds cannot be conformally immersed into the Euclidean space ${{\mathbf {E}}^4}$.

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