Geometric invariants for Seifert fibred manifolds
Author:
Ming Qing Ouyang
Journal:
Trans. Amer. Math. Soc. 346 (1994), 641659
MSC:
Primary 55R55; Secondary 55R10, 57N10, 57R20
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 ChernSimons invariant and the invariant, we also derive some elementary formulae for the ChernSimons 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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 [5]
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 [6]
 M. Hirsch, Immersion of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242276. MR 0119214 (22:9980)
 [7]
 F. Hirzebruch and D. Zagier, The AtiyahSinger theorem and elementary number theory, Publish or Perish, 1974. MR 0650832 (58:31291)
 [8]
 T. Kawasaki, The signature theorem for manifolds, Topology 17 (1978), 7583. MR 0474432 (57:14072)
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 The index of elliptic operators over manifolds, Nagoya Math. J. 84 (1981), 135157. MR 641150 (83i:58095)
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 W. Neumann and M. Jankins, Seifert manifolds, Lecture notes, Brandeis Univ., 1981.
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 I. Satake, The GaussBonnet theorem for manifolds, J. Math. Soc. Japan 9 (1957), 464493. MR 0095520 (20:2022)
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 J. Seade and B. Steer, A note on the eta function for quotients of by cocompact Fuchsian groups, Topology 26 (1987), 7991. MR 880510 (88d:58131)
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 W. Thurston, The geometry and topology of manifolds, Lecture notes, Princeton Univ., 1978.
 [16]
 W. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), 357381. MR 648524 (83h:57019)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199412576449
PII:
S 00029947(1994)12576449
Article copyright:
© Copyright 1994 American Mathematical Society
