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Cyclic branched coverings of 2-bridge knots.

Alberto Cavicchioli, Beatrice Ruini, Fulvia Spaggiari (1999)

Revista Matemática Complutense

In this paper we study the connections between cyclic presentations of groups and the fundamental group of cyclic branched coverings of 2-bridge knots. Then we show that the topology of these manifolds (and knots) arises, in a natural way, from the algebraic properties of such presentations.

Foliations and spinnable structures on manifolds

Itiro Tamura (1973)

Annales de l'institut Fourier

In this paper we study a new structure, called a spinnable structure, on a differentiable manifold. Roughly speaking, a differentiable manifold is spinnable if it can spin around a codimension 2 submanifold, called the axis, as if the top spins.The main result is the following: let M be a compact ( n - 1 ) -connected ( 2 n + 1 ) -dimensional differentiable manifold ( n 3 ) , then M admits a spinnable structure with axis S 2 n + 1 . Making use of the codimension-one foliation on S 2 n + 1 , this yields that M admits a codimension-foliation.

Higher simple structure sets of lens spaces with the fundamental group of arbitrary order

L’udovít Balko, Tibor Macko, Martin Niepel, Tomáš Rusin (2019)

Archivum Mathematicum

Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory with the fundamental group of arbitrary order. As a corollary we also obtain a calculation of the simple structure sets of the products of lens spaces and spheres of dimension grater or equal to 3 .

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...

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