scholarly journals OPEN BOOKS AND THE WEINSTEIN CONJECTURE

2014 ◽  
Vol 65 (3) ◽  
pp. 869-885 ◽  
Author(s):  
M. Dorner ◽  
H. Geiges ◽  
K. Zehmisch
Keyword(s):  
Open Books ◽  
Weinstein Conjecture

scholarly journals EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS

2006 ◽  
Vol 17 (09) ◽  
pp. 1013-1031 ◽  
Author(s):  
TOLGA ETGÜ ◽  
BURAK OZBAGCI
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Tight Contact ◽  
Weinstein Conjecture ◽  
Circle Bundles ◽  
Surface Singularities

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, on some Seifert fibered 3-manifolds we describe open books which are horizontal with respect to their plumbing description. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3-manifolds supported by planar open books. As a consequence, the Weinstein conjecture holds for these tight contact structures [1].

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

scholarly journals Open books for Boothby-Wang bundles, fibered Dehn twists and the mean Euler characteristic

2014 ◽  
Vol 12 (2) ◽  
pp. 379-426 ◽  
Author(s):  
River Chiang ◽  
Fan Ding ◽  
Otto van Koert
Keyword(s):  
Euler Characteristic ◽  
Open Books ◽  
Dehn Twists ◽  
The Mean

scholarly journals Real Polynomial Maps and Singular Open Books at Infinity

2016 ◽  
Vol 118 (1) ◽  
pp. 57 ◽  
Author(s):  
Raimundo N. Araújo Dos Santos ◽  
Ying Chen ◽  
Mihai Tibăr
Keyword(s):  
Open Book ◽  
Real Polynomial ◽  
Open Books ◽  
Polynomial Maps ◽  
Real Polynomial Maps

We provide significant conditions under which we prove the existence of stable open book structures at infinity, i.e. on spheres $S^{m-1}_R$ of large enough radius $R$. We obtain new classes of real polynomial maps $\mathsf{R}^m \to \mathsf{R}^p$ which induce such structures.

scholarly journals Legal Reasoning of Credit on Buying and Selling Gold: Mapping The Debate on 'Ilath Al-Hukm

2021 ◽  
Vol 10 (2) ◽  
pp. 295
Author(s):  
Muhammad Sholihin
Keyword(s):  
Legal Reasoning ◽  
Secondary Sources ◽  
Open Books ◽  
The Law

This paper is intended to identify the law of buying and selling gold legally. Credit and understand the illat stated to the law. The approach used in this study is more of a normative and legal juridical approach, where the study of secondary sources in the form of books, open books, and articles is carried out to obtain answers to the formulation of the problem. In general, this study has identified that gold transactions on credit among Mashab scholars are haram-mutlaq, with the illat that gold is a Ribawi commodity and is mutlaq tsammaniyah. In contrast to Ibn Taimiyah and Ibn Qayyim and the DSN-MUI fatwa, which allows it as long as gold is not used as a price or money.

FABLES FOR THE INSTRUCTION OF YOUTH PUBLISHED IN BOSTON IN 1818

PEDIATRICS ◽  
1972 ◽  
Vol 50 (1) ◽  
pp. 158-159
Author(s):  
Thomas E. Cone
Keyword(s):  
Nineteenth Century ◽  
New England ◽  
School Children ◽  
Early Years ◽  
Open Books ◽  
Moral Instruction ◽  
Almost All

In the early years of the nineteenth century William Perry's The Only Sure Guide to the English Tongue, published by Isaiah Thomas, Jr., was the most widely used speller and reader in New England schools (Fig. 1). The two things in Perry's book that were said to have most impressed those who learned to spell and read from it were the frontispiece (Fig. 2) and the collection of fables. The frontispiece shows a tree of learning growing in a schoolyard, and groups of boys playing in its shadow. A ladder reaches into the branches and several boys with open books in their hands are climbing up the ladder into branches of the tree. The illustrated fables found toward the end of Perry's book were studied and memorized by almost all New England school children a century and a half ago. Perry's choice of fables, one of which will be published each month, will offer an excellent view of the kind of moral instruction our children were once taught.1

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