Displaying similar documents to “The Knot Spectrum of Confined Random Equilateral Polygons”

Knot manifolds with isomorphic spines

Alberto Cavicchioli, Friedrich Hegenbarth (1994)

Fundamenta Mathematicae

Similarity:

We study the relation between the concept of spine and the representation of orientable bordered 3-manifolds by Heegaard diagrams. As a consequence, we show that composing invertible non-amphicheiral knots yields examples of topologically different knot manifolds with isomorphic spines. These results are related to some questions listed in [9], [11] and recover the main theorem of [10] as a corollary. Finally, an application concerning knot manifolds of composite knots with h prime factors...

High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański, Andreĭ Vesnin (1999)

Fundamenta Mathematicae

Similarity:

We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.

Characterization of knot complements in the n-sphere

Vo-Thanh Liem, Gerard Venema (1995)

Fundamenta Mathematicae

Similarity:

Knot complements in the n-sphere are characterized. A connected open subset W of S n is homeomorphic with the complement of a locally flat (n-2)-sphere in S n , n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of S 1 in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.