On the topology and analysis of a closed one form. I (Novikov's theory revisited)
| dc.creator | Burghelea, Dan | |
| dc.creator | Haller, Stefan | |
| dc.date | 2001-01-05 | |
| dc.date.accessioned | 2026-07-07T04:39:32Z | |
| dc.date.available | 2026-07-07T04:39:32Z | |
| dc.description | We consider systems $(M,ω,g)$ with $M$ a closed smooth manifold, $ω$ a real valued closed one form and $g$ a Riemannian metric, so that $(ω,g)$ is a Morse-Smale pair, Definition~2. We introduce a numerical invariant $ρ(ω,g)\in[0,\infty]$ and improve Morse-Novikov theory by showing that the Novikov complex comes from a cochain complex of free modules over a subring $Λ'_{[ω],ρ}$ of the Novikov ring $Λ_{[ω]}$ which admits surjective ring homomorphisms $\ev_s:Λ'_{[ω],ρ}\to\C$ for any complex number $s$ whose real part is larger than $ρ$. We extend Witten-Helffer-Sjöstrand results from a pair $(h,g)$ where $h$ is a Morse function to a pair $(ω,g)$ where $ω$ is a Morse one form. As a consequence we show that if $ρ<\infty$ the Novikov complex can be entirely recovered from the spectral geometry of $(M,ω,g)$. | |
| dc.description | 36 pages, 2 figures, AMSTeX | |
| dc.identifier | https://arxiv.org/abs/math/0101043 | |
| dc.identifier | http://arxiv.org/abs/math/0101043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60699 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58G26 | |
| dc.title | On the topology and analysis of a closed one form. I (Novikov's theory revisited) | |
| dc.type | text |