Casson--type invariants in dimension four

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

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Geometric Topology, 57M27; 57R58; 58D27

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http://salesiana.dossiersoluciones.com/handle/123456789/73786

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501090
 http://arxiv.org/abs/math/0501090

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arXiv