Search results for "Isotopy"

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.

Presentations for the punctured mapping class groups in terms of Artin groups

1999

Consider an oriented compact surface F of positive genus, possibly with boundary, and a finite set P of punctures in the interior of F, and define the punctured mapping class group of F relatively to P to be the group of isotopy classes of orientation-preserving homeomorphisms h: F-->F which pointwise fix the boundary of F and such that h(P) = P. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic with quotients of Artin groups by some relations involving fundamental elements of parabolic subgroups.

Origin of Blue Sapphire in Newly Discovered Spinel–Chlorite–Muscovite Rocks within Meta-Ultramafites of Ilmen Mountains, South Urals of Russia: Evide…

2019

Blue sapphire of gem quality was recently discovered in spinel&ndash

El macrotexto poético : claves para su determinación metodológica

2016

Toda metodología está llamada a abrir nuevos horizontes de lectura a quienes se acercan a leer poesía con mayor o menor intención analítica. Sin embargo, curiosamente dichos métodos han dejado de lado, en buena parte, a una realidad compositiva altamente demostrada y recurrente: los macrotextos poéticos. Se propone en este breve trabajo dar algunas de las claves metodológicas y terminológicas para analizarlos con cierta atención y profundidad, entendiendo, además, que este tipo de libros abundan en la literatura hispanoamericana a pesar de la escasa atención recibida. Sin la pretensión de querer establecer aquí un corpus poético suficientemente relevante, hemos querido aplicar, de manera or…

Isotopy classes of diffeomorphisms of (k-1)-connected almost-parallelizable 2k-manifolds

1979

Bridges, channels and Arnold's invariants for generic plane curves

2002

Abstract We define sums of plane curves that generalize the idea of connected sum and show how Arnol'd's invariants behave with respect to them. We also consider the inverse process of decomposition of a curve and as an application, obtain a new method that reduces considerably the amounts of computation involved in the calculation of Arnold's invariants.

HOMFLY-PT skein module of singular links in the three-sphere

2012

For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.

Tailoring a pair of pants

2021

Abstract We show how to deform the map Log : ( C ⁎ ) n → R n such that the image of the complex pair of pants P ∘ ⊂ ( C ⁎ ) n is the tropical hyperplane by showing an (ambient) isotopy between P ∘ ⊂ ( C ⁎ ) n and a natural polyhedral subcomplex of the product of the two skeleta S × Σ ⊂ A × C of the amoeba A and the coamoeba C of P ∘ . This lays the groundwork for having the discriminant to be of codimension 2 in topological Strominger-Yau-Zaslow torus fibrations.

Khovanov homology for signed divides

2009

The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles in a [math] –disc, one can associate a strongly invertible link in the [math] –sphere. This can be generalized to signed divides: divides with [math] or [math] sign assignment to each crossing point. Conversely, to any link [math] that is strongly invertible for an involution [math] , one can associate a signed divide. Two strongly invertible links that are isotopic through an isotopy respecting the involution are called strongly equivalent. Such isotopi…

Representative major element compositions of clinopyroxenes and phlogopites from ultrapotassic rocks from Nangqian basin (Eastern Tibet)

2020

Representative major element compositions (in wt%) of clinopyroxenes and phlogopites from Nangqian ultrapotassic rocks. In-situ major-element compositions of mineral phases were obtained using the JEOL JXA-8230 Electron Microprobe at ISTerre, University Grenoble Alpes. Analytical conditions were 15 kV accelerating voltage and 12 nA beam current. The ZAF procedure was applied to reduce the raw data. The microprobe was calibrated using natural and synthetic standards. An X-ray element map of a calcite-bearing aggregate was acquired using 15 kV accelerating voltage and 10 nA beam current.