Theoretical analysis demonstrates a Milnor fiber description of Floer homology in Brieskorn-Hamm singularities, highlighting an equivalence between Donaldson and Seiberg-Witten Casson invariants.
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.
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Lee et al. (2026) studied this question.
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