A 1-parameter Approach to Links in a Solid Torus
نویسنده
چکیده
Abstract. To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a study of codimension 2 singularities of link diagrams. For closed braids with a fixed number of strands, trace graphs can be recognized up to equivalence excluding one type of moves in polynomial time with respect to the braid length.
منابع مشابه
A Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملگرم کردن پلاسما با امواج برنشتاین الکترونی از طریق واگردانی امواج عادی و فراعادی درلایه UHR
Magnetically confined plasma can be heated with high power microwave sources. In spherical torus the electron plasma frequency exeeds the electron cyclotron frequency (EC) and, as a consequence, electromagnetic waves at fundamental and low harmonic EC cannot propagate within the plasma. In contrast, electron Bernstein waves (EBWs) readily propagate in spherical torus plasma and are absorbed str...
متن کاملPolynomial Invariants of Legendrian Links and Plane Fronts
We show that the framed versions of the Kauuman and HOMFLY poly-nomials of a Legendrian link in the standard contact 3-space and solid torus are genuine polynomials in the framing variable. This proves a series of conjectures of 5] and provides estimates for the Bennequin{Tabachnikov numbers of such links. In a series of recent papers 1{3], V. I. Arnold revived interest in the study of plane cu...
متن کاملChaos and quasi-periodicity in diffeomorphisms of the solid torus
The Hénon family of planar maps is considered driven by the Arnold family of circle maps. This leads to a five-parameter family of skew product systems on the solid torus. In this paper the dynamics of this skew product family and its perturbations are studied. It is shown that, in certain parameter domains, Hénon-like strange attractors occur. The existence of quasi-periodic Hénon-like attract...
متن کاملar X iv : m at h / 06 01 26 6 v 1 [ m at h . Q A ] 1 1 Ja n 20 06 ON THE HECKE ALGEBRAS AND THE COLORED HOMFLY POLYNOMIAL
Abstract. The colored HOMFLY polynomial is the quantum invariant of oriented links in S associated with irreducible representations of the quantum group Uq(slN). In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The te...
متن کامل