Topological Invariants

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 142)


Let K be a knotted surface in S 4. Let N(K) denote a tubular neighborhood of K, and let X = S 4\int N(X) denote the complement of the neighborhood. Let E = S 4 \ K. It is obvious that X is a deformation retract of E. We call the set X the knot exterior.


Branch Point Fundamental Group Triple Point Morse Function Commutator Subgroup 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA
  2. 2.Department of MathematicsHiroshima UniversityHigashi-Hiroshima City, HiroshimaJapan
  3. 3.Department of MathematicsUniversity of South FloridaTampaUSA

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