The Engel–Lutz twist and overtwisted Engel structures
نویسندگان
چکیده
منابع مشابه
Open Books Supporting Overtwisted Contact Structures and Stallings Twist
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called “twisting loop”. We show that the existence of a twisting loop on the fiber surface of an open book is equivalent up to positive stabilization to the existence of an overtwisted disk ...
متن کاملHolomorphic Engel Structures
Recently there has been renewed interest among differential geometers in the theory of Engel structures. We introduce holomorphic analogues of these structures, and pose the problem of classifying projective manifolds admitting them. Besides providing the basic properties of these varieties, we present two series of examples and characterize them by certain positivity conditions on the Engel st...
متن کاملExistence of Engel structures
We develop a construction of Engel structures on 4– manifolds based on decompositions of manifolds into round handles. This allows us to show that all parallelizable 4–manifolds admit an Engel structure. We also show that, given two Engel manifolds M1, M2 satisfying a certain condition on the characteristic foliations, there is an Engel structure on M1#M2#(S ×S) which is closely related to the ...
متن کاملLegendrian Ribbons in Overtwisted Contact Structures
We show that a null–homologous transverse knot K in the complement of an overtwisted disk in a contact 3–manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self–linking number of K with respect to S satisfies sl(K,S) = −χ(S). In particular, every null–homologous topological knot type in an overtwisted contact manifold can be represented...
متن کاملEngel structures with trivial characteristic foliations
Engel structures on M×S and M×I are studied in this paper, where M is a 3–dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S or I . It is proved that they are characterized by contact structures on the cross section M , the twisting numbers, and Legendrian foliations on both ends M × ∂I in the case of M × I . AMS Classification 57R25...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2020
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2020.24.2471