## Geometry & Topology

### Floer cohomology, multiplicity and the log canonical threshold

Mark McLean

#### 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 $f$.

#### Article information

Source
Geom. Topol., Volume 23, Number 2 (2019), 957-1056.

Dates
Revised: 11 August 2018
Accepted: 11 October 2018
First available in Project Euclid: 17 April 2019

https://projecteuclid.org/euclid.gt/1555466434

Digital Object Identifier
doi:10.2140/gt.2019.23.957

Mathematical Reviews number (MathSciNet)
MR3939056

Zentralblatt MATH identifier
07056057

#### Citation

McLean, Mark. Floer cohomology, multiplicity and the log canonical threshold. Geom. Topol. 23 (2019), no. 2, 957--1056. doi:10.2140/gt.2019.23.957. https://projecteuclid.org/euclid.gt/1555466434

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