title: Kindred diagrams
metadata.name: dc.contributor.author
metadata.value: Nezhinskij, Vladimir M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-12-27T13:05:53Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-12-27T13:05:53Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Nezhinskij V.M. Kindred diagrams. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 4, pp. 713–719. https://doi.org/10.21638/spbu01.2023.408 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.408
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44556
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: By a diagram we mean a topological space obtained by gluing to a standard circle a finite
  number of pairwise non-intersecting closed rectangles along their lateral sides, the glued
  rectangles are pairwise disjoint. Diagrams are not new objects; they were used in many
  areas of low-dimensional topology. Our main goal is to develop the theory of diagrams
  to a level sufficient for application in one more branch — in the theory of tangles. We
  provide the diagrams with simple additional structures — the smoothness of the circles and
  rectangles that are pairwise consistent with each other, the orientation of the circle, a point
  on the circle; we introduce new equivalence relation (that is, as far as the author knows, not
  previously encountered in the scientific literature) — kindred relation; we define a surjective
  mapping of the set of classes of kindred diagrams onto the set of classes of diffeomorphic
  smooth compact connected two-dimensional manifolds with boundary, and note that in the
  simplest cases this surjection is also a bijection. The application of the constructed theory
  to the tangle theory requires additional preparation and therefore is not included in this
  article; the author intends to devote a separate publication to this application.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 10(68); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: diagram
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: transformer
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: disk-band graph
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Kindred diagrams
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 713-719.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44556/1/713-719.pdf
resources.format: Adobe PDF
resources.size: 267,59 kB