Knot theory for self-indexed graphs

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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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Autores principales: Grana, M., Turaev, V.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00029947_v357_n2_p535_Grana
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00029947_v357_n2_p535_Grana2023-10-03T13:55:22Z Knot theory for self-indexed graphs Grana, M. Turaev, V. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Grana, M.
Turaev, V.
spellingShingle Grana, M.
Turaev, V.
Knot theory for self-indexed graphs
author_facet Grana, M.
Turaev, V.
author_sort Grana, M.
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
url http://hdl.handle.net/20.500.12110/paper_00029947_v357_n2_p535_Grana
work_keys_str_mv AT granam knottheoryforselfindexedgraphs
AT turaevv knottheoryforselfindexedgraphs
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