scholarly journals The Self-Linking Number in Planar Open Book Decompositions

2012 ◽  
Vol 19 (1) ◽  
pp. 41-58 ◽  
Author(s):  
Keiko Kawamuro
Keyword(s):  
The Self ◽  
Open Book ◽  
Linking Number ◽  
Open Book Decompositions

scholarly journals The self-linking number in annulus and pants open book decompositions

2011 ◽  
Vol 11 (1) ◽  
pp. 553-585 ◽  
Author(s):  
Keiko Kawamuro ◽  
Elena Pavelescu
Keyword(s):  
The Self ◽  
Open Book ◽  
Linking Number ◽  
Open Book Decompositions

scholarly journals Planar open book decompositions of 3-manifolds

2014 ◽  
Vol 44 (5) ◽  
pp. 1621-1630
Author(s):  
Sinem Onaran
Keyword(s):  
Open Book ◽  
Open Book Decompositions

Applications of Decomposition Theorems to Trivializing h-Cobordisms

1977 ◽  
Vol 20 (3) ◽  
pp. 389-391 ◽  
Author(s):  
Terry Lawson
Keyword(s):  
Euler Characteristic ◽  
Characteristic Zero ◽  
Closed Manifold ◽  
Geometric Proof ◽  
Open Book ◽  
Open Book Decompositions ◽  
Decomposition Theorems

AbstractA geometric proof is presented that, under certain restrictions, the product of an h-cobordism with a closed manifold of Euler characteristic zero is a product cobordism. The results utilize open book decompositions and round handle decompositions of manifolds.

scholarly journals AN INVARIANT OF LEGENDRIAN AND TRANSVERSE LINKS FROM OPEN BOOK DECOMPOSITIONS OF CONTACT 3-MANIFOLDS

2020 ◽  
pp. 1-33
Author(s):  
ALBERTO CAVALLO
Keyword(s):  
Chain Complex ◽  
Open Book ◽  
Rational Homology ◽  
Open Book Decompositions ◽  
Chain Complexes ◽  
Legendrian Links ◽  
Sum Formula ◽  
A Chain ◽  
Special Cycle ◽  
Rational Homology Sphere

Abstract We introduce a generalization of the Lisca–Ozsváth–Stipsicz–Szabó Legendrian invariant ${\mathfrak L}$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link L in a contact 3-manifold ${(M,\xi)}$ with a diagram D, given by an open book decomposition of ${(M,\xi)}$ adapted to L, and we construct a chain complex ${cCFL^-(D)}$ with a special cycle in it denoted by ${\mathfrak L(D)}$ . Then, given two diagrams ${D_1}$ and ${D_2}$ which represent Legendrian isotopic links, we prove that there is a map between the corresponding chain complexes that induces an isomorphism in homology and sends ${\mathfrak L(D_1)}$ into ${\mathfrak L(D_2)}$ . Moreover, a connected sum formula is also proved and we use it to give some applications about non-loose Legendrian links; that are links such that the restriction of ${\xi}$ on their complement is tight.

scholarly journals Notes on open book decompositions for Engel structures

2018 ◽  
Vol 18 (7) ◽  
pp. 4275-4303 ◽  
Author(s):  
Vincent Colin ◽  
Francisco Presas ◽  
Thomas Vogel
Keyword(s):  
Open Book ◽  
Open Book Decompositions ◽  
Engel Structures

COMPLEXITY OF OPEN BOOK DECOMPOSITIONS VIA ARC COMPLEX

2010 ◽  
Vol 19 (01) ◽  
pp. 55-69 ◽  
Author(s):  
TOSHIO SAITO ◽  
RYOSUKE YAMAMOTO
Keyword(s):  
Fiber Surface ◽  
Heegaard Splitting ◽  
Open Book ◽  
Open Book Decomposition ◽  
Open Book Decompositions

Based on Hempel's distance of a Heegaard splitting, we define a certain kind of complexity of an open book decomposition, called a translation distance, by using the arc complex of its fiber surface. We then show that an open book decomposition is of translation distance at most two if it is split into "simpler" open book decompositions, or at most three if it admits a Stallings twist on it.

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