Special moves for open book decompositions of 3-manifolds

被引：2

作者：

Piergallini, Riccardo ^{[1
]}

Zuddas, Daniele ^{[2
]}

机构：

[1] Univ Camerino, Scuola Sci & Tecnol, Via Madonna Carceri 9, I-62032 Camerino, Italy

[2] Univ Bayreuth, Math Inst, Lehrstuhl Math 8, NW 2,Univ Str 30, D-95447 Bayreuth, Germany

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2018年 / 27卷 / 11期

关键词：

Open book decomposition; fibered knot; fibered link; 3-manifold; Lefschetz fibration;

D O I：

10.1142/S0218216518430083

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.

引用

页数：16

共 50 条

[1] OPEN BOOK DECOMPOSITIONS OF 3-MANIFOLDS
MYERS, R
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 72 (02) : 397 - 402
[2] PLANAR OPEN BOOK DECOMPOSITIONS OF 3-MANIFOLDS
Onaran, Sinem
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2014, 44 (05) : 1621 - 1630
[3] OPEN BOOK DECOMPOSITIONS OF 3-MANIFOLDS - PRELIMINARY REPORT
MYERS, R
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (06): : A651 - A651
[4] On the Alexander polynomials of open book decompositions of 3-manifolds
Yamamoto, Ryosuke
[J]. TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (01) : 173 - 178
[5] Surgery diagrams and open book decompositions of contact 3-manifolds
Stipsicz, AI
[J]. ACTA MATHEMATICA HUNGARICA, 2005, 108 (1-2) : 71 - 86
[6] Surgery diagrams and open book decompositions of contact 3-manifolds
András I. Stipsicz
[J]. Acta Mathematica Hungarica, 2005, 108 : 71 - 86
[7] Positive open book decompositions of Stein fillable 3-manifolds along prescribed links
Ishikawa, M
[J]. TOPOLOGY, 2006, 45 (02) : 325 - 342
[8] AN INVARIANT OF LEGENDRIAN AND TRANSVERSE LINKS FROM OPEN BOOK DECOMPOSITIONS OF CONTACT 3-MANIFOLDS
Cavallo, Alberto
[J]. GLASGOW MATHEMATICAL JOURNAL, 2021, 63 (02) : 451 - 483
[9] The Casson-Walker invariant of 3-manifolds with genus one open book decompositions
Mochizuki, Atsushi
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2019, 28 (06)
[10] CELLULAR DECOMPOSITIONS OF 3-MANIFOLDS THAT YIELD 3-MANIFOLDS
ARMENTRO.S
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, (107) : 1 - &

← 1 2 3 4 5 →