#### Volume 23, issue 2 (2019)

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Floer cohomology, multiplicity and the log canonical threshold

### Mark McLean

Geometry & Topology 23 (2019) 957–1056
##### Abstract

Let $f$ be a polynomial over the complex numbers with an isolated singularity at $0$. We show that the multiplicity and the log canonical threshold of $f$ at $0$ are invariants of the link of $f$ 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 ${E}^{1}$ page is explicitly described in terms of a log resolution of $f$. 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 $f$.

##### Keywords
log canonical threshold, Floer cohomology, singularity, Zariski conjecture, multiplicity, symplectic geometry, contact geometry
##### Mathematical Subject Classification 2010
Primary: 14J17, 32S55, 53D10, 53D40