Displaying similar documents to “A new class of stuck unknots in Pol 6 .”

Knots, butterflies and 3-manifolds..

H. M. Hilden, J. M. Montesinos, D. M. Tejada, M. M. Toro (2004)

Disertaciones Matemáticas del Seminario de Matemáticas Fundamentales

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On a problem in effective knot theory

Stefano Galatolo (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The following problem is investigated: «Find an elementary function F ⁢ n : Z → Z such that if Γ is a knot diagram with n crossings and the corresponding knot is trivial, then there is a sequence of Reidemeister moves that proves triviality such that at each step we have less than F ⁢ n crossings». The problem is shown to be equivalent to a problem posed by D. Welsh in [7] and solved by geometrical techniques (normal surfaces).

Reidemeister-type moves for surfaces in four-dimensional space

Dennis Roseman (1998)

Banach Center Publications

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We consider smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in ℝ n + 2 (or S n + 2 ), for the cases n=2 or n=3. In a previous paper we have generalized the notion of the Reidemeister moves of classical knot theory. In this paper we examine in more detail the above mentioned dimensions. Examples are given; in particular we examine projections of twist-spun knots. Knot moves are given which demonstrate the triviality of the 1-twist spun trefoil. Another application...

Discrete thickness

Sebastian Scholtes (2014)

Molecular Based Mathematical Biology

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We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are deffned on equilateral polygons with n vertices. It will turn out that the smooth ropelength, which is the scale invariant quotient of length divided by thickness, is the Γ-limit of the discrete ropelength for n → ∞, regarding the topology induced by the Sobolev norm ‖ · ‖ W1,∞(S1,ℝd). This result directly implies the convergence of almost minimizers of the...