scholarly journals Open book decompositions of links of quotient surface singularities and support genus problem

2020 ◽  
Vol 5 (1) ◽  
pp. 54-78
Author(s):  
Elif Dalyan ◽  
Keyword(s):  
Open Book ◽  
Open Book Decompositions ◽  
Quotient Surface ◽  
Surface Singularities

OPEN BOOK DECOMPOSITIONS OF LINKS OF SIMPLE SURFACE SINGULARITIES

2009 ◽  
Vol 20 (12) ◽  
pp. 1527-1545 ◽  
Author(s):  
MOHAN BHUPAL
Keyword(s):  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Open Book Decompositions ◽  
Surface Singularities ◽  
Simple Surface

We describe open book decompositions of links of simple surface singularities that support the corresponding unique Milnor fillable contact structures. The open books we describe are isotopic to Milnor open books.

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

scholarly journals Infinitesimal deformations of quotient surface singularities

1988 ◽  
Vol 20 (1) ◽  
pp. 31-66 ◽  
Author(s):  
Kurt Behnke ◽  
Constantin Kahn ◽  
Oswald Riemenschneider
Keyword(s):  
Quotient Surface ◽  
Surface Singularities ◽  
Infinitesimal Deformations

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.

Sign in / Sign up

Export Citation Format

Share Document