منابع مشابه
Existence 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 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 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...
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As a consequence of identifying the principle described in the title, we prove that for any uncountable cardinal λ, if there is a λ-free Whitehead group of cardinality λ which is not free, then there are many “nice” Whitehead groups of cardinality λ which are not free.
متن کاملTHE h-PRINCIPLE FOR BROKEN LEFSCHETZ FIBRATIONS
It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to ob...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2017
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-017-0732-6