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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.40 no.2 Bogotá July./Dec. 2006
David Mond
Mathematics Institute University of Warwick Coventry CV4 7AL Warwick, England
e-mail: mond@maths.warwick.ac.uk
Abstract. An examination of the Reidemeister moves, and of the other changes which the plane projection of a space-curve undergoes on moving the centre of projection, reveals an surprising link between the changes in the homology of the image and the codimension of the singularities of projection. This link is the most accessible instance of a widespread phenomenon of singular complex geometry. This article gives a brief and non-technical survey.
Keywords and phrases. Singularities, vanishing homology, codimension.
2000 Mathematics Subject Classification. Primary: 32S05, 32S30. Secondary: 32S55.
Resumen. El estudio de los movimientos de Reidemeister, y de los demás cambios que sufre la proyección radial al plano de una curva en el espacio tridimensional, al cambiar el centro de la proyección, revela una sorprendente relación entre los cambios en la homología de la imagen, por una parte, y la codimension de las singularidades de proyección por otra. Esta es la instancia mas accesible de un fenómeno generalizado de la geometría compleja singular. El artículo hace una breve reseña, nada técnica, del fenómeno.
Dedicación: Di esta charla durante la primera visita que hice a Colombia después de la muerte del profesor Jairo Charris. Dedico este artículo al recuerdo vivo de su espíritu refulgente y generoso que nos hizo posible, a mí y a tantos otros, entrar en el mundo de la matemática.
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(Recibido enero de 2006. Aceptado en noviembre de 2006)
