Holomorphic Disks and Topological Invariants for Rational Homology Three-spheres
نویسنده
چکیده
The aim of this article is to introduce and study certain topological invariants for oriented, rational homology three-spheres Y . These groups are relatively Z-graded Abelian groups associated to SpinC structures over Y . Given a Heegaard splitting of Y = U0∪Σ U1, these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1.
منابع مشابه
Holomorphic Disks and Topological Invariants for Closed Three-manifolds
The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spinc structure t. Given a Heegaard splitting of Y = U0 ∪Σ U1, these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1.
متن کاملOn Finite Type 3-manifold Invariants V: Rational Homology 3-spheres
We introduce a notion of nite type invariants of oriented rational homology 3-spheres. We show that the map to nite type invariants of integral homology 3-spheres is one-to-one and deduce that the space of nite type invari-ants of rational homology 3-spheres is a ltered commutative algebra with nite dimensional nonzero graded quotients only in degrees divisible by 3. We show that the Casson-Wal...
متن کاملLEGENDRIAN SUBMANIFOLDS IN R2n+1 AND CONTACT HOMOLOGY
Contact homology for Legendrian submanifolds in standard contact (2n + 1)space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. The homology provides new invariants of Legendrian isotopy. These invariants show that the theory of Legendrian isotopy is very rich. For example, they detect infinite families of pairwise non-isotop...
متن کاملHeegaard diagrams and holomorphic disks
Gromov’s theory of pseudo-holomorphic disks [39] has wide-reaching consequences in symplectic geometry and low-dimensional topology. Our aim here is to describe certain invariants for low-dimensional manifolds built on this theory. The invariants we describe here associate a graded Abelian group to each closed, oriented three-manifold Y , the Heegaard Floer homology of Y . These invariants also...
متن کاملThe Perturbative Invariants of Rational Homology 3-spheres Can Be Recovered from the Lmo Invariant the Perturbative Invariants of Rational Homology 3-spheres Can Be Recovered from the Lmo Invariant
We show that the perturbative g invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra g, i.e., the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13, 14, 15], this implies that the LMO in...
متن کامل