The Compressibility of Checkerboard Surfaces of Link Diagrams  

作　　者：Zhi Qiang BAO 

机构地区：[1]LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第10期1845-1858,共14页数学学报（英文版）

基　　金：Partially supported by NSFC(Grant No.10201002);Partially supported by JSPS(Research No.P03189)

摘　　要：Consider the checkerboard surfaces defined by some link diagrams. When they are not orientable, one considers the boundary surfaces of small regular neighborhoods of them. This article studies the compressibility problem of these kinds of surfaces in the link complements. The problem is solved by devising a normalization theory for the compressing discs, which brings up an algorithm to read out compressibility directly from the link diagrams. As an application of the algorithm, the compressibility changes under Reidermeister moves are studied. Diagrams from the knot tables are also studied, and surprisingly, some of them are shown to define completely compressible surfaces of this kind. Infinitely many examples of non-alternating knot diagrams with incompressible surfaces of this kind are also constructed.Consider the checkerboard surfaces defined by some link diagrams. When they are not orientable, one considers the boundary surfaces of small regular neighborhoods of them. This article studies the compressibility problem of these kinds of surfaces in the link complements. The problem is solved by devising a normalization theory for the compressing discs, which brings up an algorithm to read out compressibility directly from the link diagrams. As an application of the algorithm, the compressibility changes under Reidermeister moves are studied. Diagrams from the knot tables are also studied, and surprisingly, some of them are shown to define completely compressible surfaces of this kind. Infinitely many examples of non-alternating knot diagrams with incompressible surfaces of this kind are also constructed.

关 键 词：COMPRESSIBILITY checkerboard surface knot diagram 

分 类 号：O157.5[理学—数学]