• Corpus ID: 252438703

On PFH and HF spectral invariants

  title={On PFH and HF spectral invariants},
  author={Guanheng Chen},
In this note, we define the link spectral invariants by using the cylindrical formulation of the quantitative Heegaard Floer homology. We call them HF spectral invariants. We deduce a relation between the HF spectral invariants and the PFH spectral invariants by using closed-open morphisms and open-closed morphisms. For the sphere, we prove that the homogenized HF spectral invariants at the unit are equal to the homogenized PFH spectral invariants. Moreover, we show that the homogenized PFH… 

Figures from this paper



Closed-open morphisms on periodic Floer homology

In this note, we investigate homomorphisms from the periodic Floer homology (PFH) to the quantitative Heegaard Floer homology. We call the homomorphisms closed–open morphisms. Under certain

PFH spectral invariants on the two-sphere and the large scale geometry of Hofer's metric

We resolve three longstanding questions related to the large scale geometry of the group of Hamiltonian diffeomorphisms of the twosphere, equipped with Hofer’s metric. Namely: (1) we resolve the

Spectral invariants for monotone Lagrangians

Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper [73], they have been defined in various contexts, mainly via Floer homology

On cobordism maps on periodic Floer homology

In this article, we investigate the cobordism maps on periodic Floer homology (PFH). In the first part of the paper, we define the cobordism maps on PFH via Seiberg Witten theory as well as the

Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces

In previous work, we defined “link spectral invariants” for any compact surface and used these to study the algebraic structure of the group of area-preserving homeomorphisms; in particular, we showed

Periodic Floer homology and Seiberg-Witten Floer cohomology

Various Seiberg-Witten Floer cohomologies are defined for a closed, oriented 3-manifold; and if it is the mapping torus of an area-preserving surface automorphism, it has an associated periodic Floer

Applications of higher-dimensional Heegaard Floer homology to contact topology

The goal of this paper is to set up the general framework of higher-dimensional Heegaard Floer homology, define the contact class, and use it to give an obstruction to the Liouville fillability of a

A Lagrangian Piunikhin-Salamon-Schwarz Morphism and Two Comparison Homomorphisms in Floer Homology

In this article we address two issues. First, we explore to what extent the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] an

Cobordism maps on periodic Floer homology induced by elementary Lefschetz fibrations

Embedded contact homology and Seiberg–Witten Floer cohomology II

This is a sequel to four earlier papers by the author that construct an isomorphism between the embedded contact homology and Seiberg‐Witten Floer cohomology of a compact 3‐manifold with a given