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Article

$\mathbb{S}\text{ol}^{3}\times \mathbb{E}^{1}$ -MANIFOLDS

  • J. A. HILLMAN (a1)
Abstract

We show that closed $\mathbb{S}\text{ol}^{3}\times \mathbb{E}^{1}$ -manifolds are Seifert fibred, with general fibre the torus, and base one of the flat 2-orbifolds $T,Kb,\mathbb{A},\mathbb{M}b,S(2,2,2,2),P(2,2)$ or $\mathbb{D}(2,2)$ , and outline how such manifolds may be classified.

Copyright
© 2017 Australian Mathematical Publishing Association Inc. 
References
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[1] Cobb, R., ‘Infrasolvmanifolds of dimension four’, PhD Thesis, School of Mathematics and Statistics, University of Sydney, 1999.
[2] Dekimpe, K., Almost Bieberbach Groups: Affine and Polynomial Structures, Lecture Notes in Mathematics, 1639 (Springer, Berlin, 1996).
[3] Hillman, J. A., Four-Manifolds, Geometries and Knots, GT Monographs, 5 (Geometry and Topology Publications, Coventry, 2002), revised in 2007 and 2014.
[4] Hillman, J. A., ‘Geometries and infrasolvmanifolds in dimension 4’, Geom. Dedicata (2007), 57–72.
[5] Hillman, J. A., ‘The F2 -cohomology rings of Sol3 -manifolds’, Bull. Aust. Math. Soc. 89 (2014), 191–201.
[6] Lee, K. B. and Thuong, S., ‘Infra-solvmanifolds of Sol1 4 ’, J. Korean Math. Soc. 52 (2015), 1209–1251.
[7] Montesinos, J. M., Classical Tessellations and Three-Manifolds, Universitext (Springer, Berlin, 1987).
[8] Raghunathan, M., Discrete Subgroups of Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Folge 2, Bd 68 (Springer, Berlin, 1972).
[9] Sakamoto, K. and Fukuhara, S., ‘Classification of T 2 -bundles over T 2 ’, Tokyo J. Math. 6 (1983), 311–327.
[10] Wall, C. T. C., ‘Geometric structures on compact complex analytic surfaces’, Topology 25 (1986), 119–153.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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