Defining an SU(3)-Casson/U(2)-Seiberg-Witten integer invariant for integral homology 3-spheres
Yuhan Lim
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.
Create a lesson
Related papers
Topological and spectral rigidity of hypersurface Zoll manifolds
Gustavo Martins
Stationary varifolds with singularities II
Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al.
Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities
Mitchell Gaudet
Deformations of harmonic maps with conical singularities
Dominik Gutwein, Thibault Langlais
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song