Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Simple knots without unique minimal surfaces


Author: Herbert C. Lyon
Journal: Proc. Amer. Math. Soc. 43 (1974), 449-454
MSC: Primary 55A25
DOI: https://doi.org/10.1090/S0002-9939-1974-0377850-8
MathSciNet review: 0377850
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct infinitely many simple knots and infinitely many nonsimple knots, all of genus one, and all having both knotted and unknotted minimal spanning surfaces. The complements of the simple knots all contain closed incompressible surfaces of genus two.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55A25

Retrieve articles in all journals with MSC: 55A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0377850-8
Keywords: Incompressible surface, knot, knot space, knotted minimal surface, nonunique minimal surface, simple knot, unknotted minimal surface
Article copyright: © Copyright 1974 American Mathematical Society