TY - JOUR

T1 - The first-order genus of a knot

AU - Horn, Peter D.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=57549116905&partnerID=8YFLogxK

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U2 - 10.1017/S0305004108001886

DO - 10.1017/S0305004108001886

M3 - Article

AN - SCOPUS:57549116905

VL - 146

SP - 135

EP - 149

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -