ISSN:
1432-1297
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary An alternating link ℒ Г is canonically associated with every finite, connected, planar graph Γ. The natural ideal polyhedral decomposition of the complement of ℒ Г is investigated. Natural singular geometric structures exist onS 3−ℒ Г , with respect to which the geometry of the cusp has a shape reflecting the combinatorics of the underlying link projection. For the class of ‘balanced graphs’, this induces a flat structure on peripheral tori modelled on the tessellation of the plane by equilateral triangles. Examples of links containing immersed, closed π1-injective surfaces in their complements are given. These surfaces persist after ‘most’ surgeries on the link, the resulting closed 3-manifolds consequently being determined by their fundamental groups.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01232034
