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k-Invariants of knotted 2-spheres

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: S.P. Plotnick, A.I. Suciu

Editorial: Commentarii Mathematici Helvetici, 60 (1), p.54-84, 1985.


This paper studies some questions concerning homotopy type invariants of smooth four-dimensional knot complements. Higher-dimensional knot theory diverges sharply from classical knot theory in this respect. A knot complement $S^4setminus S^2$ has the homotopy type of a $3$-complex, so a natural question is whether the homotopy theory of knot complements in $S^4$ can be as complicated as that of arbitrary $3$-complexes. The main result of this paper indicates that the answer is yes.

Cuvinte cheie: Knots in the 4-sphere, k-invariants