embedded contact homology造句

例句与造句

1. Taubes has shown that it is isomorphic to embedded contact homology.
2. He gave an invited talk at the International Congress of Mathematicians in 2010, entitled " Embedded contact homology and its applications ".
3. More recently, Taubes, C . Kutluhan and Y-J . Lee proved that embedded contact homology is isomorphic to Heegaard Floer homology.
4. The dynamics of the Reeb field can be used to study the structure of the contact manifold or even the underlying manifold using techniques of Floer homology such as embedded contact homology.
5. In particular, the proof provides a shortcut to the closely related program of proving the Weinstein conjecture by showing that the embedded contact homology of any contact three-manifold is nontrivial.
6. It's difficult to find embedded contact homology in a sentence. 用embedded contact homology造句挺难的
7. Embedded contact homology has now been proven to be isomorphic to both monopole Floer homology ( Kutluhan-Lee-Taubes ) and Heegaard Floer homology ( Colin-Ghiggini-Honda ).
8. He is known for proving the double bubble conjecture on the shape of two-chambered soap bubbles, and for his work circle-valued Morse theory and on embedded contact homology, which he defined.
9. An analog of embedded contact homology may be defined for mapping tori of symplectomorphisms of a surface ( possibly with boundary ) and is known as periodic Floer homology, generalizing the symplectic Floer homology of surface symplectomorphisms.
10. In the case of embedded contact homology, one obtains an invariant of the underlying three-manifold, i . e . the embedded contact homology is independent of contact structure; this allows one to obtain results that hold for any Reeb vector field on the manifold.
11. In the case of embedded contact homology, one obtains an invariant of the underlying three-manifold, i . e . the embedded contact homology is independent of contact structure; this allows one to obtain results that hold for any Reeb vector field on the manifold.
12. The main body of his work involves embedded contact homology, or ECH . ECH is a holomorphic curve model for the Seiberg-Witten-Floer homology of a three-manifold, and is thus a version of Taubes's Gromov invariant for certain four-manifolds with boundary.
13. Expanding both on this and on the equivalence of the Seiberg Witten and Gromov invariants, Taubes has also proven ( in a long series of preprints, beginning with ) that a contact 3-manifold's embedded contact homology is isomorphic to a version of its Seiberg Witten Floer cohomology.
14. Ozsvath and Szabo used constructed it for Heegaard Floer homology using Giroux's relation between contact manifolds and open book decompositions, and it comes for free, as the homology class of the empty set, in embedded contact homology . ( Which, unlike the other three, requires a contact homology for its definition . 0For embedded contact homology see .)
15. Ozsvath and Szabo used constructed it for Heegaard Floer homology using Giroux's relation between contact manifolds and open book decompositions, and it comes for free, as the homology class of the empty set, in embedded contact homology . ( Which, unlike the other three, requires a contact homology for its definition . 0For embedded contact homology see .)