The non-orientable 4-genus of 11 crossing non-alternating knots

被引：0

作者：

Fairchild, Megan ^{[1
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70802 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2025年 / 34卷 / 01期

关键词：

Topology; knot theory; non-orientable; 4-genus; crosscap number; prime knots; non-oriented band move; slice knots; double branched cover; arf invariant; knot signature Goeritz matrix; checkerboard coloring; non-alternating knots; linking form; NUMBER;

D O I：

10.1142/S0218216524500500

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The non-orientable 4-genus of a knot K in S3 is defined to be the minimum first Betti number of a non-orientable surface F smoothly embedded in B4 so that K bounds F. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We will also view obstructions to a knot bounding a M & ouml;bius band given by the double branched cover of S3 branched over K.

引用

页数：26

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