Geometric invariants for Seifert fibred $3$-manifolds
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- by Ming Qing Ouyang
- Trans. Amer. Math. Soc. 346 (1994), 641-659
- DOI: https://doi.org/10.1090/S0002-9947-1994-1257644-9
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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 ${{\mathbf {E}}^4}$.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 346 (1994), 641-659
- MSC: Primary 55R55; Secondary 55R10, 57N10, 57R20
- DOI: https://doi.org/10.1090/S0002-9947-1994-1257644-9
- MathSciNet review: 1257644