A monopole homology of integral homology 3-spheres

dc.creatorLi, Weiping
dc.date2000-03-22
dc.date.accessioned2026-07-07T04:34:23Z
dc.date.available2026-07-07T04:34:23Z
dc.descriptionTo 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.description20 pages, AMSLaTeX
dc.identifierhttps://arxiv.org/abs/math/0003134
dc.identifierhttp://arxiv.org/abs/math/0003134
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58884
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.titleA monopole homology of integral homology 3-spheres
dc.typetext

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