The Kauffman bracket skein module of a twist knot exterior

被引：14

作者：

Bullock, Doug ^{[1
]}

Lo Faro, Walter

机构：

[1] Boise State Univ, Dept Math, Boise, ID 83725 USA

[2] Univ Wisconsin, Dept Math, Stevens Point, WI 54481 USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2005年 / 5卷

关键词：

knot; link; skein module; Kauffman bracket;

D O I：

10.2140/agt.2005.5.107

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compute the Kauffman bracket skein module of the complement of a twist knot, finding that it is free and infinite dimensional. The basis consists of cables of a two-component link, one component of which is a meridian of the knot. The cabling of the meridian can be arbitrarily large while the cabling of the other component is limited to the number of twists.

引用

收藏

页码：107 / 118

页数：12

相关论文

共 16 条

[1] On the Kauffman bracket skein module of surgery on a trefoil [J].

Bullock, D .

PACIFIC JOURNAL OF MATHEMATICS, 1997, 178 (01) :37-51

[2] Rings of SL2(C)-characters and the Kauffman bracket skein module [J].

Bullock, D .

COMMENTARII MATHEMATICI HELVETICI, 1997, 72 (04) :521-542

[3] A finite set of generators for the Kauffman bracket skein algebra [J].

Bullock, D .

MATHEMATISCHE ZEITSCHRIFT, 1999, 231 (01) :91-101

[4] THE (2,INFINITY)-SKEIN MODULE OF THE COMPLEMENT OF A (2,2P+1) TORUS KNOT [J].

BULLOCK, D .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1995, 4 (04) :619-632

[5] Understanding the Kauffman bracket skein module [J].

Bullock, D ;

Frohman, C ;

Kania-Bartoszynska, J .

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1999, 8 (03) :265-277

[6] The A-polynomial from the noncommutative viewpoint [J].

Frohman, C ;

Gelca, R ;

Lofaro, W .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (02) :735-747

[7]

Hoste, 1993, J KNOT THEOR RAMIF, V02, P321

[8] THE KAUFFMAN BRACKET SKEIN MODULE OF S(1)XS(2) [J].

HOSTE, J ;

PRZYTYCKI, JH .

MATHEMATISCHE ZEITSCHRIFT, 1995, 220 (01) :65-73

[9] The hyperbolic volume of knots from the quantum dilogarithm [J].

Kashaev, RM .

LETTERS IN MATHEMATICAL PHYSICS, 1997, 39 (03) :269-275

[10]

LOFARO W, 1998, THESIS U IOWA