Let be a polynomial over the complex numbers with an isolated singularity at . We show that the multiplicity and the log canonical threshold of at are invariants of the link of viewed as a contact submanifold of the sphere.
This is done by first constructing a spectral sequence converging to the fixed-point Floer cohomology of any iterate of the Milnor monodromy map whose page is explicitly described in terms of a log resolution of . This spectral sequence is a generalization of a formula by A’Campo. By looking at this spectral sequence, we get a purely Floer-theoretic description of the multiplicity and log canonical threshold of .
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