Instanton Floer homology and Milnor Fibers

In the early days of the Floer theory, Atiyah asked if there is a Milnor fiber description of the Floer homology of the links of singularities. We answer this question for the Brieskorn-Hamm complete intersection singularities. The resulting combinatorial formulas lead to an independent proof of the...

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Hauptverfasser: Lee, Kyoung-Seog, Libgober, Anatoly, Saveliev, Nikolai
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Sprache:eng
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Zusammenfassung:In the early days of the Floer theory, Atiyah asked if there is a Milnor fiber description of the Floer homology of the links of singularities. We answer this question for the Brieskorn-Hamm complete intersection singularities. The resulting combinatorial formulas lead to an independent proof of the equality of the Casson invariants in the Donaldson and Seiberg-Witten theories. We use similar techniques to express the Heegaard Floer d-invariant of torus knots in terms of their Milnor fibers.
DOI:10.48550/arxiv.2410.16584