legendrian造句

• There can be inequivalent Legendrian knots that are isotopic as topological knots.
• Two Legendrian knots are equivalent if they are isotopic through a family of Legendrian knots.
• Two Legendrian knots are equivalent if they are isotopic through a family of Legendrian knots.
• This has yielded noncontractible loops of Legendrian knots which are contractible in the space of all knots.
• SFT also associates a relative invariant of a Legendrian submanifold of a contact manifold known as relative contact homology.
• This Chekanov-Eliashberg invariant yields an invariant for loops of Legendrian knots by considering the monodromy of the loops.
• The set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilizations is in bijection with the set of transverse knots.
• The set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilizations is in bijection with the set of transverse knots.
• Legendrian submanifolds are very rigid objects; typically there are infinitely many Legendrian isotopy classes of embeddings which are all smoothly isotopic.
• Legendrian submanifolds are very rigid objects; typically there are infinitely many Legendrian isotopy classes of embeddings which are all smoothly isotopic.
• He obtained his Ph . D . at Moscow State University in 1977 ( the thesis : " Lagrangian and Legendrian singularities " ).
• Any Legendrian knot can be " C " 0-perturbed in a direction transverse to the contact planes to obtain a transverse knot.
• This yields a bijection between the set of isomorphism classes of transverse knots and the set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilization.
• This yields a bijection between the set of isomorphism classes of transverse knots and the set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilization.
• Symplectic field theory provides invariants of Legendrian submanifolds called relative contact homology that can sometimes distinguish distinct Legendrian submanifolds that are topologically identical ( i . e . smoothly isotopic ).
• Symplectic field theory provides invariants of Legendrian submanifolds called relative contact homology that can sometimes distinguish distinct Legendrian submanifolds that are topologically identical ( i . e . smoothly isotopic ).
• Yuri Chekanov developed a purely combinatorial version of relative contact homology for Legendrian knots, i . e . a combinatorially defined invariant that reproduces the results of relative contact homology.
• Many inequivalent Legendrian knots can be distinguished by considering their Thurston-Bennequin invariants and rotation number, which are together known as the " classical invariants " of Legendrian knots.
• Many inequivalent Legendrian knots can be distinguished by considering their Thurston-Bennequin invariants and rotation number, which are together known as the " classical invariants " of Legendrian knots.
• His Ph . D . thesis and several other papers concern Legendrian knots, and his best-known work applies symplectic field theory to derive invariants of ( topological ) knots.