Work

Instanton Floer homology and Milnor fibers

Year: 2026

Type: article

Abstract: 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.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-026-04110-8

Authors: Kyoung-Seog Lee, Anatoly Libgober, Nikolai Saveliev

Institutions: Pohang University of Science and Technology, University of Illinois Chicago, University of Miami

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation