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The first-order genus of a knot

Published online by Cambridge University Press:  01 January 2009

PETER D. HORN
PETER D. HORN*
Affiliation:
Mathematics Department, Rice University, 6100 S. Main St., Houston, TX 77005-1892, U.S.A. e-mail: [email protected]
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Abstract

We introduce a geometric invariant of knots in S3, called the first-order genus, that is derived from certain 2-complexes called gropes, and we show it is computable for many examples. While computing this invariant, we draw some interesting conclusions about the structure of a general Seifert surface for some knots.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 135 - 149
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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