A monopole homology for integral homology 3-spheres

Authors : Weiping LI

Pages : 125-160

View : 16 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded insert ignore into journalissuearticles values(monopole); homology MH*insert ignore into journalissuearticles values(Y, Ihinsert ignore into journalissuearticles values(Q; h0);); whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow Ihinsert ignore into journalissuearticles values(Q; h0);, where Q is the unique Uinsert ignore into journalissuearticles values(1);-reducible monopole of the Seiberg-Witten equation on Y and h0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH*insert ignore into journalissuearticles values(Y, Ihinsert ignore into journalissuearticles values(Q; h0);); is invariant among Riemannian metrics with same Ihinsert ignore into journalissuearticles values(Q; h0);. This provides a chamber-like structure for the monopole homology of integral homology 3-spheres. The assigned function MHSWF: \{Ihinsert ignore into journalissuearticles values(Q; h0);\} \to \{MH*insert ignore into journalissuearticles values(Y, Ihinsert ignore into journalissuearticles values(Q; h0););\} is a topological invariant insert ignore into journalissuearticles values(as Seiberg-Witten-Floer Theory);.
Keywords : Turk J Math, 27, 2003, , 125 160 Turk J Math, vol 27, iss 1