All three-manifolds are pullbacks of a branched covering ๐ยณ to ๐ยณ
All three-manifolds are pullbacks of a branched covering ๐ยณ to ๐ยณ
There are two main results in this paper. First, we show that every closed orientable <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 can be constructed by taking a pair of disjoint bounded orientable surfaces in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S cubed"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> โฆ