scholarly journals Topological entropy for Reeb vector fields in dimension three via open book decompositions

2019 ◽  
Vol 6 ◽  
pp. 119-148
Author(s):  
Marcelo R.R. Alves ◽  
Vincent Colin ◽  
Ko Honda
Keyword(s):  
Topological Entropy ◽  
Vector Fields ◽  
Open Book ◽  
Reeb Vector ◽  
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
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