Slides of the plenary talk by Samuel Lomonaco - GW Links
Slides of the plenary talk by Samuel Lomonaco - GW Links
Slides of the plenary talk by Samuel Lomonaco - GW Links
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4-D Analog <strong>of</strong> <strong>the</strong> Apspericity <strong>of</strong> Knots ?For 1-knots,asphericity implies <strong>the</strong> exteriorX is an Eilenberg-MacLanespace, i.e.,X K 1X,1Question. Want can be said about analog<strong>of</strong> Papa’s ashphericity <strong>the</strong>orem for 2-knots?4-D Analog <strong>of</strong> <strong>the</strong> Apspericity <strong>of</strong> Knots ?S , kS4 2Def. A 2-knotis said to be quasi-aspherical (QA) if <strong>the</strong> third homology group <strong>of</strong><strong>the</strong> universal cover <strong>of</strong> its exterior vanishes.Theorem. (<strong>Lomonaco</strong>) Ifis QA,<strong>the</strong>n <strong>the</strong> homotopy type <strong>of</strong> its exterior X isdetermined <strong>by</strong> its algebraic 3-type, i.e., <strong>by</strong><strong>the</strong> triple consisting <strong>of</strong>:• X 1 • X 2 as a X 1• The first k-invariant3H 1X;2XS , kS4 2-modulekXlying inEdwin Abbott’s FlatlandThe Cross sectionalApproach to 2-Knots3-D LandThe MidsectionRepresentation2-Knots10
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