Cambridge University Press eBooks· 2020· Book chapter
Introduction: Motivation
- 2,278citations
- 2020year
Short summary
This introduction motivates a book on symplectic topology by highlighting intersection theory's role in two early theorems, one of which requires a nonobvious extension of homological intersection theory.
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Key points
- Intersection theory is central to early theorems in symplectic topology.
- A theorem on symplectic 4-manifolds requires an extension of homological intersection theory.
- This extension specifically applies to punctured holomorphic curves.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2020 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics