Quantum Homology of fibrations over $S^2$
| dc.creator | McDuff, Dusa | |
| dc.date | 1999-05-14 | |
| dc.date.accessioned | 2026-07-07T05:29:05Z | |
| dc.date.available | 2026-07-07T05:29:05Z | |
| dc.description | This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits additively as the vector space tensor product $H^*(M)\otimes H^*(S^2)$, and investigates conditions under which the ring structure also splits, thus generalizing work of Lalonde-McDuff-Polterovich and Seidel. The main tool is a study of certain operations in the quantum homology of the total space $P$ and of the fiber $M$, whose properties reflect the relations between the Gromov-Witten invariants of $P$ and $M$. In order to establish these properties we further develop the language introduced in [Mc3] to describe the virtual moduli cycle (defined by Liu-Tian, Fukaya-Ono, Li-Tian, Ruan and Siebert). | |
| dc.description | 53 pages, Latex document | |
| dc.identifier | https://arxiv.org/abs/math/9905092 | |
| dc.identifier | http://arxiv.org/abs/math/9905092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78506 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53 C 15 | |
| dc.title | Quantum Homology of fibrations over $S^2$ | |
| dc.type | text |