Witten-Helffer-Sjostrand Theory for a Generalized Morse Functions
| dc.creator | Wai, Hon-kit | |
| dc.date | 1995-03-14 | |
| dc.date.accessioned | 2026-07-07T09:12:30Z | |
| dc.date.available | 2026-07-07T09:12:30Z | |
| dc.description | In this paper, we extend the Witten-Helffer-Sjöstrand theory from Morse functions to generalized Morse functions. In this case, the spectrum of the Witten deformed Laplacian $Δ(t)$, for large t, can be seperated into the small eigenvalues (which tend to 0 as $t\rightarrow\infty$), large and very large eigenvalues (both of which tend to $\infty$ as $t\rightarrow\infty$). The subcomplex $Ω_{0}^{\ast}(M,t)$ spanned by eigenforms corresponding to the small and large eigenvalues of $Δ(t)$ is finite dimensional. Under some mild conditions, it is shown that $(Ω_{0}^{\ast}(M,t),d(t))$ converges to a geometric complex associated to the generalized Morse function as $t\rightarrow\infty$. | |
| dc.description | LATex,26 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9503006 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9503006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152040 | |
| dc.subject | Differential Geometry | |
| dc.title | Witten-Helffer-Sjostrand Theory for a Generalized Morse Functions | |
| dc.type | text |