English

Casson--type invariants in dimension four

Geometric Topology 2007-05-23 v1

Abstract

This article surveys our ongoing project about the relationship between invariants extending the classical Rohlin invariant of homology spheres and those coming from 4-dimensional (Yang-Mills) gauge theory. The main conjecture towards which this project is directed is that the Rohlin invariant and the gauge theoretic invariant coincide for a homology S1×S3S^1\times S^3. We discuss the implications of this conjecture for some classical problems in low-dimensional topology, and progress we have made towards proving the conjecture.

Keywords

Cite

@article{arxiv.math/0501090,
  title  = {Casson--type invariants in dimension four},
  author = {Daniel Ruberman and Nikolai Saveliev},
  journal= {arXiv preprint arXiv:math/0501090},
  year   = {2007}
}

Comments

30 pages, 5 figures. To appear in Proceedings of the Fields-McMaster Conference on Geometry and Topology of Manifolds