Geometric invariants for Seifert fibred -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 -invariant of the signature operator for some circle bundles over Riemannian -orbifolds. We then apply it to Seifert fibred -manifolds endowed with one of the six Seifert geometries. By using a relation between the Chern-Simons invariant and the -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 .

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DOI:
https://doi.org/10.1090/S0002-9947-1994-1257644-9

Article copyright:
© Copyright 1994
American Mathematical Society