Knot theory for self-indexed graphs

We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure,...

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Detalles Bibliográficos
Autor principal: Graña, Matías Alejo
Publicado: 2005
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v357_n2_p535_Grana
http://hdl.handle.net/20.500.12110/paper_00029947_v357_n2_p535_Grana
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00029947_v357_n2_p535_Grana
record_format dspace
spelling paper:paper_00029947_v357_n2_p535_Grana2023-06-08T14:23:39Z Knot theory for self-indexed graphs Graña, Matías Alejo We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We call a self-indexed graph with integral flow a comte. The analogy with links allows us to define transformations of comtes generalizing the Reidemeister moves on link diagrams. We show that many invariants of links can be generalized to comtes, most notably the linking number, the Alexander polynomials, the link group, etc. We also discuss finite type invariants and quandle cocycle invariants of comtes. Fil:Grana, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v357_n2_p535_Grana http://hdl.handle.net/20.500.12110/paper_00029947_v357_n2_p535_Grana
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We call a self-indexed graph with integral flow a comte. The analogy with links allows us to define transformations of comtes generalizing the Reidemeister moves on link diagrams. We show that many invariants of links can be generalized to comtes, most notably the linking number, the Alexander polynomials, the link group, etc. We also discuss finite type invariants and quandle cocycle invariants of comtes.
author Graña, Matías Alejo
spellingShingle Graña, Matías Alejo
Knot theory for self-indexed graphs
author_facet Graña, Matías Alejo
author_sort Graña, Matías Alejo
title Knot theory for self-indexed graphs
title_short Knot theory for self-indexed graphs
title_full Knot theory for self-indexed graphs
title_fullStr Knot theory for self-indexed graphs
title_full_unstemmed Knot theory for self-indexed graphs
title_sort knot theory for self-indexed graphs
publishDate 2005
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v357_n2_p535_Grana
http://hdl.handle.net/20.500.12110/paper_00029947_v357_n2_p535_Grana
work_keys_str_mv AT granamatiasalejo knottheoryforselfindexedgraphs
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