On the Lusternik-Schnirelmann category of symplectic manifolds and the Arnold conjecture
| dc.creator | Rudyak, Yuli B. | |
| dc.creator | Oprea, John | |
| dc.date | 1997-08-11 | |
| dc.date.accessioned | 2026-07-07T09:13:17Z | |
| dc.date.available | 2026-07-07T09:13:17Z | |
| dc.description | We prove that the Lusternik-Schnirelmann category $cat(M)$ of a closed symplectic manifold $(M, ω)$ equals the dimension $dim(M)$ provided that the symplectic cohomology class vanishes on the image of the Hurewicz homomorphism. This holds, in particular, when $π_2(M)=0$. The Arnold conjecture asserts that the number of fixed points of a Hamiltonian symplectomorphism of $M$ is greater than or equal to the number of critical points of some function on $M$. A modified form of the conjecture, replacing the latter quantity (via Lusternik-Schnirelmann theory) by $cup(M) + 1$, has been proved recently by various authors using techniques of Floer. The first author has also recently shown that the original form of the conjecture holds when $cat(M) =dim(M)$. Thus, this paper completes the proof of the original Arnold conjecture for closed symplectic manifolds with, for example, $π_2(M)=0$. | |
| dc.description | AMSTEX, 5 pages, submitted to Math. Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9708007 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9708007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152274 | |
| dc.subject | Differential Geometry | |
| dc.title | On the Lusternik-Schnirelmann category of symplectic manifolds and the Arnold conjecture | |
| dc.type | text |