Defining an SU(3)-Casson/U(2)-Seiberg-Witten integer invariant for integral homology 3-spheres
Differential Geometry
2007-05-23 v1 Geometric Topology
Abstract
The SU(3)-Casson invariant for integral homology 3-spheres as studied by Boden-Herald possesses a 'spectral flow obstruction' to being an integer valued invariant which depends only on the non-degenerate (perturbed) moduli space of flat SU(3)-connections. This obstruction is the non-trivial spectral flow of a family of twisted signature operators in 3-dimensions. The parallel U(2)-Seiberg-Witten construction also has an obstruction but from the non-trivial spectral flow of a family of twisted Dirac operators. By taking the SU(3)-flat and U(2)-Seiberg-Witten equations simultaneously the obstructions can be made to cancel and an integer invariant is obtained.
Keywords
Cite
@article{arxiv.math/0411024,
title = {Defining an SU(3)-Casson/U(2)-Seiberg-Witten integer invariant for integral homology 3-spheres},
author = {Yuhan Lim},
journal= {arXiv preprint arXiv:math/0411024},
year = {2007}
}
Comments
51pp