Search results for "57M05"

showing 3 items of 3 documents

Three-page encoding and complexity theory for spatial graphs

2004

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.

Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Algebra and Number TheoryDegree (graph theory)Semigroup010102 general mathematicsGeometric topologyGeometric Topology (math.GT)01 natural sciences57M25 57M15 57M05Combinatorics010104 statistics & probabilityMathematics - Geometric TopologyCone (topology)Additive functionEncoding (memory)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: Mathematics0101 mathematicsUnit (ring theory)Ambient isotopyMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsofComputing_DISCRETEMATHEMATICS

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Geometric représentations of the braid groups

2010

We show that the morphisms from the braid group with n strands in the mapping class group of a surface with a possible non empty boundary, assuming that its genus is smaller or equal to n/2 are either cyclic morphisms (their images are cyclic groups), or transvections of monodromy morphisms (up to multiplication by an element in the centralizer of the image, the image of a standard generator of the braid group is a Dehn twist, and the images of two consecutive standard generators are two Dehn twists along two curves intersecting in one point). As a corollary, we determine the endomorphisms, the injective endomorphisms, the automorphisms and the outer automorphism group of the following grou…

[ MATH ] Mathematics [math]rigidité[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]morphisme de monodromieiﬁcation de Nielsen Thurstonbraid groupGroup Theory (math.GR)[MATH] Mathematics [math]groupe de difféotopies[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]monodromieFOS: Mathematicssurface[MATH]Mathematics [math]représentation géométriquetransvectionmonodromymapping class groupMathematics::Geometric TopologyrigidityNielsen-Thurstongroupe de tressesAMS Subject Classiﬁcation: Primary 20F38 57M07. Secondary 57M99 20F36 20E36 57M05.mapping groupMathematics - Group Theorygroupe de diﬀétopies

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PERIPHERALLY SPECIFIED HOMOMORPHS OF LINK GROUPS

2005

Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic characterization of all possible peripheral structures in certain homomorphic images of link groups.

Pure mathematicsAlgebra and Number TheoryLink groupGeometric Topology (math.GT)Mathematics::Geometric TopologyMathematics - Geometric Topology57M0557M25FOS: MathematicsAlgebraic Topology (math.AT)57M25; 57M05Mathematics - Algebraic TopologyAlgebraic numberNuclear ExperimentKnot (mathematics)MathematicsJournal of Knot Theory and Its Ramifications

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