CIRCULAR HANDLE DECOMPOSITIONS OF FREE GENUS ONE KNOTS

被引：2

作者：

Manjarrez-Gutierrez, Fabiola ^{[1
]}

Nunez, Victor ^{[1
]}

Ramirez-Losada, Enrique ^{[1
]}

机构：

[1] CIMAT, Guanajuato 36000, Mexico

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2015年 / 275卷 / 02期

关键词：

circular thin position; free genus; free genus one knots; Seifert surfaces; handle decompositions; almost fibered; TUNNEL NUMBER;

D O I：

10.2140/pjm.2015.275.361

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine the structure of the circular handle decompositions of the family of free genus one knots. Namely, if k is a free genus one knot, then the handle number h (k) = 0, 1 or 2, and, if k is not fibered (that is, if h (k) > 0), then k is almost fibered. For this, we develop practical techniques to construct circular handle decompositions of knots with free Seifert surfaces in the 3-sphere (and compute handle numbers of many knots), and, also, we characterize the free genus one knots with more than one Seifert surface. These results are obtained through analysis of spines of surfaces on handle-bodies. Also we show that there are infinite families of free genus one knots with either h (k) = 1 or h (k) = 2.

引用

页码：361 / 407

页数：47

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