The Su(3) Casson Invariant for 3-manifolds Split along a 2-sphere or a 2-torus
نویسنده
چکیده
We describe the deenition of the SU(3) Casson invariant and outline an argument which determines the contribution of certain types of components of the at moduli space. Two applications of these methods are detailed. The rst is a connect sum formula for the SU(3) Casson invariant 3]. The second presents a strategy for computing the SU(3) Casson invariant for certain graph manifolds.
منابع مشابه
Splitting the Spectral Flow and the Su(3) Casson Invariant for Spliced Sums
We show that the SU(3) Casson invariant for spliced sums along certain torus knots equals 16 times the product of their SU(2) Casson knot invariants. The key step is a splitting formula for su(n) spectral flow for closed 3-manifolds split along a torus.
متن کاملA Symplectic Geometry Approach to Generalized Casson's Invariants of 3-manifolds
1. In 1985 lectures at MSRI, Andrew Casson introduced an integer valued invariant À(M) for any oriented integral homology 3-sphere M. This invariant has many remarkable properties; detailed discussions of some of these can be found in an exposé by S. Akbulut and J. McCarthy (see [AM]). Roughly, A(M) measures the 'oriented' number of irreducible representations of the fundamental group n{(M) in ...
متن کاملM ay 2 00 2 A CONNECTED SUM FORMULA FOR THE SU ( 3 ) CASSON INVARIANT HANS
We provide a formula for the SU(3) Casson invariant for 3-manifolds given as the connected sum of two integral homology 3-spheres.
متن کاملThe Casson and Rohlin Invariants of Homology 3-tori
Casson’s introduction of his invariant for homology 3–spheres [1, 18] has had many profound consequences in low-dimensional topology. One of the most important is the vanishing of the Rohlin invariant of a homotopy sphere, which follows from Casson’s identification of his invariant, modulo 2, with the Rohlin invariant of an arbitrary homology sphere. The proof of this identification proceeds vi...
متن کاملThe Casson and Rohlin Invariants of Homology 3-tori Daniel Ruberman and Nikolai Saveliev
Casson’s introduction of his invariant for homology 3–spheres [1, 18] has had many profound consequences in low-dimensional topology. One of the most important is the vanishing of the Rohlin invariant of a homotopy sphere, which follows from Casson’s identification of his invariant, modulo 2, with the Rohlin invariant of an arbitrary homology sphere. The proof of this identification proceeds vi...
متن کامل