Betti number [SEP] named after
which tells us the maximum amount of cuts that must be made before separating a surface into two pieces or 0-cycles, 1-cycles, etc. These numbers are used today in fields such as simplicial homology, computer science, digital images, etc.
The term "Betti numbers" was coined by Henri Poincaré after Enrico Betti. The modern formulation is due to Emmy Noether.
Definitions.
Informally, the "k"th Betti number refers to the number of "k"-dimensional holes on a topological surface. The first few Betti numbers
Arnold–Givental conjecture
The Arnold–Givental conjecture, named after Vladimir Arnold and Alexander Givental, is a statement on Lagrangian submanifolds. It gives a lower bound in terms of the Betti numbers of on the number of intersection points of with a Hamiltonian isotopic Lagrangian submanifold which intersects transversally.
Let be a smooth family of Hamiltonian functions of and denote by the one-time map of the flow of the Hamiltonian vector field of . Let be a Lagrangian submanifold, invariant under some antisymplectic involution of . Assume that and intersect