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Full-Text Articles in Physical Sciences and Mathematics
Characterization Of Knot Complements In The 4-Sphere, Vo Thanh Liem, Gerard A. Venema
Characterization Of Knot Complements In The 4-Sphere, Vo Thanh Liem, Gerard A. Venema
University Faculty Publications and Creative Works
Knot complements in S4 are characterized as follows: A connected open set W ⊂ S4 is homeomorphic to the complement of some locally flat 2-sphere in S4 if and only if H1(W) is infinite cyclic, W has one end, and the fundamental group of that end is infinite cyclic. Applications include a characterization of weakly flat 2-spheres in S4 and a complement theorem for 2-spheres in S4.