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Infinite group actions on spheres.

Gaven J. Martin (1988)

Revista Matemática Iberoamericana

This paper is mainly intended as a survey of the recent work of a number of authors concerning certain infinite group actions on spheres and to raise some as yet unanswered questions. The main thrust of the current research in this area has been to decide what topological and geometrical properties characterise the infinite conformal or Möbius groups. One should then obtain reasonable topological or geometrical restrictions on a subgroup G of the homeomorphism group of a sphere which will imply...

Local moves on knots and products of knots

Louis H. Kauffman, Eiji Ogasa (2014)

Banach Center Publications

We show a relation between products of knots, which are generalized from the theory of isolated singularities of complex hypersurfaces, and local moves on knots in all dimensions. We discuss the following problem. Let K be a 1-knot which is obtained from another 1-knot J by a single crossing change (resp. pass-move). For a given knot A, what kind of relation do the products of knots, K ⊗ A and J ⊗ A, have? We characterize these kinds of relation between K ⊗ A and J ⊗ A by using local moves on high...

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