Intersection Pairings on Conley Indices.

Intro -- Contents -- Introduction -- Chapter 1. Basic Notation and Background Definitions -- A. Basic Notation -- B. The Conley Index -- C. Homology and Cohomology of Conley Indices -- D. Sign Conventions for Products in Homology and Cohomology -- Chapter 2. TheIntersection Pairings L, L, and [sup(#)]L -- A. Pairs of Index Pairs Admissible for the Intersection Pairing -- B. The Euclidean Case: the Homology Intersection Number Pairing L -- C. The Manifold Case: the Intersection Class and NumberPairings L and [(sup(#)]L -- Chapter 3. Statement of the Continuation Results and Examples -- A. Invariance of Intersection Numbers under Continuation -- B. Continuation of £ over a Path of Isolated Invariant Sets -- Chapter 4. Construction of Bilinear Pairings on Conley Indices -- A. The Existence of Admissible Pairs of Index Pairs -- B. Functorially Produced Pairings on the Conley Indices -- C. The Proofs of Theorems 2.4 and 2.11 -- Chapter 5. Proofs of the Continuation Results -- A. Maps between Conley Indices from Paths of Invariant Sets -- B. The Proofs of Theorems 3.1, 3.2, 3.3, and 3.7 -- Chapter 6. Some Basic Computational Tools -- A. Conditions on Singular Cycles for Computing L and [sup(#)]L -- B. The Behavior of £ under Orbit Preserving Maps -- Chapter 7. L for Normally Hyperbolic Invariant Submanifolds -- A. Summary of Results -- B. Computational Preliminaries -- C. Results Leading to the Proof of Theorem 7.5 -- D. Results Leading to the Proof of Theorem 7.6 -- Chapter 8. Products of Intersection Pairings -- A. Preliminary Observations and Definitions -- B. Conley Indices of Product Invariant Sets -- C. A Kunneth Theorem for Conley Indices -- D. Factor and Product Intersection Pairings -- Chapter 9. The Cap Product Representation of L and the Nonsingularity of [sup(#)]L -- A. The Cap Product Representation and Corollaries.

B. Some Technical Propositions on Poincare Duality Isomorphisms and Cech Cap Products -- C. Results Leading to the Proof of Theorem 9.4 -- D. The Case S ∩ ∂ M ≠ θ -- Appendix A. Intersection Numbers and Existence Results for Two-Point Boundary Value Problems of Singularly Perturbed Systems -- Appendix B. Proofs of the Propositions in 9.B -- References.

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