A monopole homology of integral homology 3-spheres
| dc.creator | Li, Weiping | |
| dc.date | 2000-03-22 | |
| dc.date.accessioned | 2026-07-07T04:34:23Z | |
| dc.date.available | 2026-07-07T04:34:23Z | |
| dc.description | To an integral homology 3-sphere $Y$, we assign a well-defined $\Z$-graded (monopole) homology $MH_*(Y, I_{\e}(\T; \e_0))$ whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow $I_{\e}(\T; \e_0)$, where $\T$ is the unique U(1)-reducible monopole of the Seiberg-Witten equation on $Y$ and $\e_0$ is a reference perturbation datum. The definition uses the moduli space of monopoles on $Y \x \R$ introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology $MH_*(Y, I_{\e}(\T; \e_0))$ is invariant among Riemannian metrics with same $I_{\e}(\T; \e_0)$. This provides a chamber-like structure for the monopole homology of integral homology 3-spheres. The assigned function $MH_{SWF}: \{I_{\e}(\T; \e_0)\} \to \{MH_*(Y, I_{\e}(\T; \e_0))\}$ is a topological invariant (as Seiberg-Witten-Floer Theory). | |
| dc.description | 20 pages, AMSLaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0003134 | |
| dc.identifier | http://arxiv.org/abs/math/0003134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58884 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.title | A monopole homology of integral homology 3-spheres | |
| dc.type | text |