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On three-manifolds dominated by circle bundles

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Abstract

We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of S 2 × S 1. This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.

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Authors and Affiliations

  1. Mathematisches Institut, LMU München, Theresienstr. 39, 80333, München, Germany

    D. Kotschick & C. Neofytidis

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  1. D. Kotschick
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  2. C. Neofytidis
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Correspondence to D. Kotschick.

Additional information

We are grateful to J. Bowden and to P. Derbez for helpful discussions. This paper was completed during a visit of D. Kotschick to the Institut Mittag-Leffler (Djursholm, Sweden). C. Neofytidis is supported by the Deutscher Akademischer Austausch Dienst (DAAD).

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Kotschick, D., Neofytidis, C. On three-manifolds dominated by circle bundles. Math. Z. 274, 21–32 (2013). https://doi.org/10.1007/s00209-012-1055-3

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  • DOI: https://doi.org/10.1007/s00209-012-1055-3

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