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Geometric invariants for Seifert fibred $ 3$-manifolds


Author: Ming Qing Ouyang
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
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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}$.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1257644-9
Article copyright: © Copyright 1994 American Mathematical Society

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