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Displaying 81 – 100 of 196

A proof of Tait’s Conjecture on prime alternating $-$ achiral knots

Nicola Ermotti, Cam Van Quach Hongler, Claude Weber (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating $-$ achiral knots:Let $K$ be a prime alternating $-$ achiral knot. Then there exists a minimal projection $Π$ of $K$ in $S^{2} \subset S^{3}$ and an involution $ϕ : S^{3} \to S^{3}$ such that:1) $ϕ$ reverses the orientation of $S^{3}$ ;2) $ϕ (S^{2}) = S^{2}$ ;3) $ϕ (Π) = Π$ ;4) $ϕ$ has two fixed points on $Π$ and hence reverses the orientation of $K$ .The purpose of this paper is to prove this statement.For the historical...

A rational noncommutative invariant of boundary links.

Garoufalidis, Stavros, Kricker, Andrew (2004)

Geometry & Topology

A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion

Yoshikazu Yamaguchi (2008)

Annales de l’institut Fourier

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $λ$ -regular $SU (2)$ or $SL (2, ℂ)$ -representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a $2$ -bridge knot and $SU (2)$ -representations of its knot group.

A Relative cohomological invariant for group pairs.

M.G.C. Andrade, E.L.C. Fanti (1994)

Manuscripta mathematica

A remark on subgroups of infinite index in Poincaré duality groups.

R. Strebel (1977)

Commentarii mathematici Helvetici

A search method for thin positions of links.

Heath, Daniel J., Kobayashi, Tsuyoshi (2005)

Algebraic & Geometric Topology

A self-linking invariant of virtual knots

Louis H. Kauffman (2004)

Fundamenta Mathematicae

This paper introduces a self-linking invariant for virtual knots and links, and relates this invariant to a state model called the binary bracket, and to a class of coloring problems for knots and links that include classical coloring problems for cubic graphs.

A Semigroup of Simple Homotopy Types.

Allan J. Sieradski (1977)

Mathematische Zeitschrift

A short proof of Eilenberg and Moore’s theorem

Maria Nogin (2007)

Open Mathematics

In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.

A short proof of the uniqueness of Kühnel's 9-vertex complex projective plane.

Bagchi, Bhaskar, Datta, Basudeb (2001)

Advances in Geometry

A simpler construction of volume polynomials for a polyhedron.

Lawrencenko, Serge, Negami, Seiya, Sabitov, Idjad Kh. (2002)

Beiträge zur Algebra und Geometrie

A spelling theorem for staggered generalized 2-complexes, with applications.

J. Howie, S.J. Pride (1984)

Inventiones mathematicae

A Splicing formula for Casson-Walker's invariant.

G. Fujita (1993)

Mathematische Annalen

A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of $S U (2)$ connections.

Himpel, Benjamin (2005)

Geometry & Topology

A Splitting Theorem for Manifolds.

Sylvain E. Cappell (1976)

Inventiones mathematicae

A stably free nonfree module and its relevance for homotopy classification, case $Q_{2} 8$ .

Beyl, F.Rudolf, Waller, Nancy (2005)

Algebraic & Geometric Topology

A Surgery Sequence in Dimension Four; The Relations with Knot Concordance.

Michael H. Freedman (1982)

Inventiones mathematicae

A SURVEY OF SEMIGROUPS OF CONTINUOUS SELFMAPS.

K.D. jr. Magill (1975)

Semigroup forum

A topological model of site-specific recombination that predicts the knot and link type of DNA products

Karin Valencia (2014)

Banach Center Publications

This is a short summary of a topological model of site-specific recombination, a cellular reaction that creates knots and links out of circular double stranded DNA molecules. The model is used to predict and characterise the topology of the products of a reaction on double stranded DNA twist knots. It is shown that all such products fall into a small family of Montesinos knots and links, meaning that the knot and link type of possible products is significantly reduced, thus aiding their experimental...

A topological version of Bertini's theorem

Artur Piękosz (1995)

Annales Polonici Mathematici

We give a topological version of a Bertini type theorem due to Abhyankar. A new definition of a branched covering is given. If the restriction $π_{V} : V \to Y$ of the natural projection π: Y × Z → Y to a closed set V ⊂ Y × Z is a branched covering then, under certain assumptions, we can obtain generators of the fundamental group π₁((Y×Z).

Currently displaying 81 – 100 of 196

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