Lagrangian Subspaces: Intersection Theory, and the Morse Index Theorem in Finite Dimensions |
Contents
Linear Symplectic Structures on Banach | 5 |
Topological | 39 |
and Intersection Theory | 50 |
Copyright | |
2 other sections not shown
Common terms and phrases
admits Ax,y Banach space boundary CALIFORNIA/SANTA CRUZ closed complement completes the proof conjugate index conjugate points CRUZ The University curve of lagrangian Darboux decomposition decreasing defined definition denotes dense diffeomorphic dim Ker eigenvalue eigenvalue curves elliptic operators finite dimensional finite dimensions follows Graph hence Hilbert space homeomorphic homotopy equivalence identified integer intersection number intersection theory isomorphism kernel L₂ lagrangian grassmannian lagrangian subspaces Lemma linear symplectic structure Maslov Cycle Maslov Index Morse Index Morse Index Theorem open set orbit orthogonal projection Proposition result SANTA CRUZ Schauder basis Section 1.1 self-adjoint operator sequence simply Sp E,w Sp H Sp(E splits strictly increasing subgroup submanifold subset Suppose symmetric bilinear forms symplectic form symplectic group symplectic space symplectic structure tangent space topology trivial University Library UNIVERSITY UNIVERSITY OF CALIFORNIA UNIVERSITY OF CALIFORNIA/SANTA vector bundle zero χε