Minimal genus in 4-manifolds with a free circle action

Mathematics – Geometric Topology

Scientific paper

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20 pages

Scientific paper

Let N be a closed irreducible 3-manifold such that its fundamental group is virtually RFRS. Using work of Ian Agol we will improve, for all but finitely many circle bundles M over N, the adjunction inequality for the minimal complexity of embedded surfaces. Appealing to a result of Dani Wise, this allows us to completely determine the minimal complexity of embedded surfaces in all but finitely many circle bundles over a large class of hyperbolic 3-manifolds.

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