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- W2765676432 abstract "Proof. Let S be the planar, meridional surface in S N (K) given by the line in Figure 2. We will show that S is incompressible. Theorem 4 then gives the result. The surface S divides (S,K) into two 3–string tangles. Each tangle is one of the three given by the (equal) tangle diagrams shown in Figure 3. If S is not incompressible, there is a compressing disc for S in one tangle. This disc is disjoint from K, and so separates the three strings. The string in bold in Figure 3 is separated from at least one of the other two. We will show that no such disc can exist. By the rotational symmetry of the tangle, we only need to consider the case where we delete the string on the left of the tangle diagram in the top right of Figure 3. This leaves the tangle (B, T ) given by the diagram DT in Figure 4. Note that DT is strongly alternating (see Figure 5)." @default.
- W2765676432 created "2017-11-10" @default.
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- W2765676432 date "2012-11-24" @default.
- W2765676432 modified "2023-09-23" @default.
- W2765676432 title "The complement of a dodecahedral knot contains an essential closed surface" @default.
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