The Extension of Knot Groups to Tangles
نویسنده
چکیده
The extension of the knot group π1(S 3 \ K) to the category of tangles is introduced via a new category-theoretic construction. Through this presentation, a new avenue of proof for results about knot groups is opened.
منابع مشابه
From 3-moves to Lagrangian tangles and cubic skein modules
We present an expanded version of four talks describing recent developments in Knot Theory to which the author contributed. We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups. The method of Burnside groups of links was discovered and developed only half a year after the last talk ...
متن کاملAbout Some Infinite Family of 2-bridge Knots and 3-manifolds
We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots ( +1)2 or ( +1)1, that are the closure of the rational (2 −1)/( −1)–tangles or (2 −1)/ –tangles, respectively.
متن کاملPersistently Laminar Tangles
We show how to build tangles T in a 3-ball with the property that any knot obtained by tangle sum with T has a persistent lamination in its exterior, and therefore has property P. The construction is based on an example of a persistent lamination in the exterior of the twist knot 61, due to Ulrich Oertel. We also show how the construction can be generalized to n-string tangles.
متن کاملVitamin E therapy prevents the accumulation of congophilic amyloid plaques and neurofibrillary tangles in the hippocampus in a rat model of Alzheimer’s disease
Objective(s): Vitamin E may have beneficial effects on oxidative stress and Aβ-associated reactive oxygen species production in Alzheimer’s disease. But, the exact role of vitamin E as a treatment for Alzheimer’s disease pathogenesis still needs to be studied. Hence, we examined the therapeutic effects of vitamin E on the density of congophilic amyloid plaques and neur...
متن کاملRational Structure on Algebraic Tangles and Closed Incompressible Surfaces in the Complements of Algebraically Alternating Knots and Links
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface with boundary in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles....
متن کامل