Casson--type invariants in dimension four

Details Casson--type invariants in dimension four Casson--type invariants in dimension four

2005-01-06

arxiv.org/abs/math/0501090v1

Mathematics

Geometric Topology

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

Scientific paper

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 $S^1\times S^3$. We discuss the implications of this conjecture for some classical problems in low-dimensional topology, and progress we have made towards proving the conjecture.

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