Geometry & Topology
- Geom. Topol.
- Volume 23, Number 2 (2019), 957-1056.
Floer cohomology, multiplicity and the log canonical threshold
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 .
Geom. Topol., Volume 23, Number 2 (2019), 957-1056.
Received: 7 March 2018
Revised: 11 August 2018
Accepted: 11 October 2018
First available in Project Euclid: 17 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J17: Singularities [See also 14B05, 14E15] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 53D10: Contact manifolds, general 53D40: Floer homology and cohomology, symplectic aspects
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