Mathematics – Geometric Topology
Scientific paper
2000-03-22
Mathematics
Geometric Topology
20 pages, AMSLaTeX
Scientific paper
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).
No associations
LandOfFree
A monopole homology of integral homology 3-spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A monopole homology of integral homology 3-spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A monopole homology of integral homology 3-spheres will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-475425