Knot theory for self-indexed graphs
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- by Matías Graña and Vladimir Turaev PDF
- Trans. Amer. Math. Soc. 357 (2005), 535-553 Request permission
Abstract:
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.References
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Additional Information
- Matías Graña
- Affiliation: Departamento de Matemática - FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
- Email: matiasg@dm.uba.ar
- Vladimir Turaev
- Affiliation: IRMA, CNRS - Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cedex, France
- Email: turaev@math.u-strasbg.fr
- Received by editor(s): July 4, 2003
- Published electronically: August 19, 2004
- Additional Notes: The work of the first author was supported by CONICET (Argentina)
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 535-553
- MSC (2000): Primary 57M25, 57M15; Secondary 05C99
- DOI: https://doi.org/10.1090/S0002-9947-04-03625-6
- MathSciNet review: 2095622