An intersection theory count of the -representations of the fundamental group of a 3-manifold
MetadataShow full item record
We define an invariant of closed 3-manifolds counting the signed equivalence classes of representations of the fundamental group in . The invariant is an -analog of the Casson-Walker invariant for SU(2). We reinterpret the invariant algebro-geometrically and show that it is non-negative. We relate the invariant to a generalization of the norm of Culler, Gordon, Luecke and Shalen. We show that an analog of the Casson-Walker knot invariant exists in this setting. We obtain a Dehn surgery formula for the invariant for manifolds which are the result of Dehn surgery on knots in integral homology spheres, where the surgery coefficients obey certain technical conditions.
Curtis, C. (2001). An intersection theory count of the SL2(C) -representations of the fundamental group of a 3-manifold. Topology, 40(4), 773-787.
File not available for download due to copyright restrictions