Abstract
The introduction motivates the remainder of the book via two specific examples of theorems from the early days of symplectic topology in which intersection theory plays a prominent role. We sketch closely analogous proofs of both theorems, emphasizing the way that intersection theory is used, but point out why the second theorem (on symplectic 4-manifolds that are standard near infinity) requires a nonobvious extension of homological intersection theory to punctured holomorphic curves. We then discuss informally some of the properties this theory will need to have and what kinds of subtle issues may arise.
Keywords
Symplectic geometrySketchMathematical proofIntersection (aeronautics)Intersection theoryMathematicsExtension (predicate logic)Pure mathematicsInfinityHolomorphic functionPoint (geometry)Topology (electrical circuits)Algebra over a fieldComputer scienceMathematical analysisGeometryCombinatoricsAlgorithmGeography
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Publication Info
- Year
- 2020
- Type
- book-chapter
- Pages
- 1-10
- Citations
- 2277
- Access
- Closed
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Cite This
Chris Wendl
(2020).
Introduction: Motivation.
Cambridge University Press eBooks
, 1-10.
https://doi.org/10.1017/9781108608954.002
Identifiers
- DOI
- 10.1017/9781108608954.002