Zeros of closed 1-forms, homoclinic orbits, and Lusternik - Schnirelman theory
| dc.creator | Farber, Michael | |
| dc.date | 2001-06-07 | |
| dc.date | 2001-06-25 | |
| dc.date.accessioned | 2026-07-07T04:42:02Z | |
| dc.date.available | 2026-07-07T04:42:02Z | |
| dc.description | In this paper we study topological lower bounds on the number of zeros of closed 1-forms without Morse type assumptions. We prove that one may always find a representing closed 1-form having at most one zero. We introduce and study a generalization $cat(X,ξ)$ of the notion of Lusternik - Schnirelman category, depending on a topological space $X$ and a cohomology class $ξ\in H^1(X;\R)$. We prove that any closed 1-form has at least $cat(X,ξ)$ zeros assuming that it admits a gradient-like vector field with no homoclinic cycles. We show that the number $cat(X,ξ)$ can be estimated from below in terms of the cup-products and higher Massey products. This paper corrects some statements made in my previous papers on this subject. | |
| dc.description | 34 pages. A refernce added | |
| dc.identifier | https://arxiv.org/abs/math/0106046 | |
| dc.identifier | http://arxiv.org/abs/math/0106046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61604 | |
| dc.subject | Differential Geometry | |
| dc.subject | Dynamical Systems | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 37Cxx, 58Exx, 53Dxx | |
| dc.title | Zeros of closed 1-forms, homoclinic orbits, and Lusternik - Schnirelman theory | |
| dc.type | text |