morse inequality造句

• These facts can be strengthened to obtain the "'Morse inequalities " ':
• The existence of Morse homology " explains ", in the sense of categorification, the Morse inequalities.
• Witten's work gave a physical proof of a classical result, the Morse inequalities, by interpreting the theory in terms of supersymmetric quantum mechanics.
• Vladimir Arnold conjectured that the number of fixed points of a generic Hamiltonian diffeomorphism of a compact symplectic manifold ( " M ", " ? " ) should be bounded from below by some topological constant of " M ", which is analogous to the Morse inequality.
• From the fact that the Morse homology is isomorphic to the singular homology, the Morse inequalities follow by considering the number of generators & mdash; that is, critical points & mdash; necessary to generate the homology groups of the appropriate ranks ( and by considering truncations of the Morse complex, to get the stronger inequalities ).