Abstract
Let (X, ω) be a symplectic rational surface. We study the space of tamed almost complex structures Jω using a fine decomposition via smooth rational curves and a relative version of the infinite dimensional Alexander- Pontrjagin duality. This decomposition provides new understandings of both the variation and the stability of the symplectomorphism group Symp(X, ω) when deforming ω In particular, we compute the rank of π1(Symp(X, ω)) with X(X) ≥ 7 in terms of the number Nω of (-2)-symplectic sphere classes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 561-606 |
| Number of pages | 46 |
| Journal | Pacific Journal of Mathematics |
| Volume | 304 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 Mathematical Sciences Publishers.
Keywords
- Almost complex structure
- Lagrangian root system
- Rational symplectic manifold
- Symplectomorphism group