Finite covers of 3-manifolds containing essential surfaces of Euler characteristic =0
Finite covers of 3-manifolds containing essential surfaces of Euler characteristic =0
We give a short proof and a slight generalization of a theorem of John Luecke, that a compact connected orientable irreducible <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="3"> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding="application/x-tex">3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifold containing an essential torus is finitely covered by a torus bundle or manifolds with unbounded first Betti …