Abstract

MONTOYA-VEGA, Gabriel. A first look at knot theory and Khovanov homology. Integración - UIS [online]. 2023, vol.41, n.2, pp.103-123.  Epub Aug 09, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v41n2-2023003.

The mathematical theory of knots studies the embeddings of circles into the space ℝ3. The introduction of homology theories results in complex mathematical structures that generate new research opportunities. In this article, we offer a first look into Khovanov homology, the long exact sequence of Khovanov homology, and we present a summary of the historical origins of the theory. Moreover, we use this sequence to calculate the homology of torus knots T (2, n). One of the the main objectives in publishing this article is to popularize knot theory and Khovanov homology in Colombia and Latin-America in general.

Keywords : Knots and links; bracket polynomial; Khovanov homology; long exact sequence of Khovanov homology; torus knots.

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