Crosscap numbers and the Jones polynomial

被引：12
作者：
Kalfagianni, Efstratia [1 ]
Lee, Christine Ruey Shan [2 ]
机构：
[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA
来源：
ADVANCES IN MATHEMATICS | 2016年 / 286卷
基金：
美国国家科学基金会;
关键词：
Alternating knot; Jones polynomial; Crosscap number (non-orientable genus); Normal surfaces; Spanning surfaces; Augmented links; COMPUTATIONAL-COMPLEXITY; KNOT; VOLUME; GENUS; DECOMPOSITIONS; SURFACES; LINKS;
D O I：
10.1016/j.aim.2015.09.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give sharp two-sided linear bounds of the crosscap number (non-orientable genus) of alternating links in terms of their Jones polynomial. Our estimates are often exact and we use them to calculate the crosscap numbers for several infinite families of alternating links and for several alternating knots with up to twelve crossings. We also discuss generalizations of our results for classes of non-alternating links. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：308 / 337
页数：30
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