Nudos y Superficies
History and Overview
2024-12-31 v1 Geometric Topology
Abstract
These notes are an introduction to knot theory from the perspective of surfaces. The notes cover fundamental concepts such as isotopies, Reidemeister moves, torus knots, and (orientable, connected) surfaces with one boundary component. They also present knot invariants defined through Seifert surfaces and their associated matrices, including the 3-genus, the Alexander polynomial, and the signature. Finally, starting from the notion of concordance and the connected sum operation, a group structure on the set of knots is introduced.
Keywords
Cite
@article{arxiv.2412.20945,
title = {Nudos y Superficies},
author = {Yoseth Arciniegas Barreto and Nicol Bermudez Bohorquez and Juanita Pinzón-Caicedo and Luisa Rozo Posada},
journal= {arXiv preprint arXiv:2412.20945},
year = {2024}
}
Comments
These are lecture note for the mini-course "Nudos y Superficies'' part of the first ECOGyT that took place in Bogot\'a on Julio de 2024, in Spanish language