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Fundamental groups of the complements to codimension 2 submanifolds of sphere. (English. Russian original) Zbl 0988.57001
Grigorchuk, R. I. (ed.), Dynamical systems, automata, and infinite groups. Transl. from the Russian. Moscow: MAIK Nauka/Interperiodica Publishing, Proc. Steklov Inst. Math. 231, 271-280 (2000); translation from Tr. Mat. Inst. Steklova 231, 284-293 (2000).
Summary: A purely algebraic description is given for the set of the fundamental groups of the complements of codimension 2 submanifolds in a $$k$$-dimensional sphere $$S^k$$, $$k\geq 4$$. This description is a generalization of the well-known Wirtinger presentation of knot groups to the $$k$$-dimensional case.
For the entire collection see [Zbl 0981.00006].
##### MSC:
 57M05 Fundamental group, presentations, free differential calculus 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 55Q52 Homotopy groups of special spaces 57M25 Knots and links in the $$3$$-sphere (MSC2010)
##### Keywords:
Wirtinger presentation; knot groups