We work in the Polyhedral Category as defined in [3], which consists of polyhedra and polymaps. A polyhedron is a space with a maximal nonempty family of p.l. related triangulations and a polymap is p.l. w.r.t. these triangulations. An ambient isotopy of a polyhedron X is a level-preserving homeo, H: XXI->XXI with H\XXl = l, Ht: X-^X for tEI is the homeo induced by H\XXt. An isotopy of Y in X i...

Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling and relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (resp. contractible open 3-manifold) M if and only if M is homeomorphic to S 3 (resp. R 3). A...

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link up to link homotopy can be cancelled in a (componentwise) connected sum with another link. In this paper we address the question whether some form of the ‘complexity accumulation’ property of knots holds for (piecewiselinear) links up to some stronger analogue of link homotopy, which still do...

This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relations is proved and necessary and sufficient conditions for the isotopy stabil...

We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion h(t, z) of a finite subset E of the Riemann sphere C parameterized by a pointed hyperbolic Riemann surface (X, t0). We prove that if this holomorphic motion has a guiding quasiconformal isotopy, then it can be extended to a new holomorphic motion of E ∪ {p} for any point p...