Casson--type invariants in dimension four

Daniel Ruberman; Nikolai Saveliev

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Casson--type invariants in dimension four

Daniel Ruberman·Nikolai Saveliev

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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 $S^1\times S^3$. 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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Daniel Ruberman, Nikolai Saveliev. 2005-01-06. Casson--type invariants in dimension four. https://arxiv.org/abs/math/0501090

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