Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 41 No. 2 (2023): Revista Integración, temas de matemáticas
Research and Innovation Articles

A first look at knot theory and Khovanov homology

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Gabriel Montoya-Vega
CUNY Graduate Center
DOI: https://doi.org/10.18273/revint.v41n2-2023003

Published 2023-11-17

Keywords

  • Knots and links,
  • bracket polynomial,
  • Khovanov homology,
  • long exact sequence of Khovanov homology,
  • torus knots

How to Cite

Montoya Vega, G. (2023). A first look at knot theory and Khovanov homology. Revista Integración, Temas De matemáticas, 41(2), 103–123. https://doi.org/10.18273/revint.v41n2-2023003

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Abstract

The mathematical theory of knots studies the embeddings of circles into the space R^3. The introduction of homology theories results in complex mathematical structures that generate new research opportunities. In this article, we oer a rst 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 LatinAmerica in general.

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