Topological extension of Calabi invariants and non-simpleness of the area preserving homeomorphism group of the disc

Topological extension of Calabi homomorphism and non-simpleness of the area-preserving homeomorphism group of two-disc

The paper contains a silly mistake in the usage of the equation (5.4) in the formula (6.5). Due to this mistake, the effect of the transfer map $phi$ is nullified. I am deeply sorry for not being very careful in my submission and making this mistake.

Extension of Calabi homomorphism and non-simpleness of the area preserving homeomorphism group of $D^2$

The content of this paper has no mathematical flaw except that the proof of the main theorem relies on the homotopy invariance of spectral invariants of topological Hamiltonian paths. Since the latter is still up in the air, the main result of the paper is the reduction of the extension problem of the Calabi homomorphism to the group of hameomorphism is still conjectural.

The group of Hamiltonian homeomorphisms and continuous Hamiltonian flows

In this paper, we study the dynamical aspects of the \emph{Hamiltonian homeomorphism group} $Hameo(M,ω)$ which was introduced by Müller and the author. We introduce the notion of autonomous continuous Hamiltonian flows and extend the well-known conservation of energy to such flows. The definitions of the Hofer length and of the spectral invariants $ρ_a$ are extended to continuous Hamiltonian paths, and the Hofer norm and the spectral norm $γ:Ham(M,ω) \to \R_+$ are generalized to the corresponding intrinsic norms on $Hameo(M,ω)$ respectively. Using these extensions, we also extend the construct…

纽结谱不变量的次领头渐近行为与曲面的同胚群

Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces

本文研究亏格为零的曲面上纽结谱不变量的次领头渐近行为，证明其对光滑含时哈密顿量有界、对有限临界值自治圆盘映射可恢复Ruelle不变量，并推导了Calabi同态的延拓性质与hameomorphism群上Calabi同态核的非单性。

定量 Heegaard Floer 上同调与 Calabi 不变量

Quantitative Heegaard Floer cohomology and the Calabi invariant

本文在任意亏格紧致曲面上定义与 Lagrangian links 相关的新谱不变量，证明其极限恢复 Calabi 不变量，并借此解决 Hamiltonian 同胚群非单性、Calabi 同态延拓及二维球面 quasimorphisms 构造等问题。

Continuous Hamiltonian dynamics and area-preserving homeomorphism group of $D^2$

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^Ω(D^2,\partial D^2)$ of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism ${\rm Cal}:Diff^Ω(D^1,\partial D^2) \to \mathbb R$ to a homomorphism $\overline{\rm Cal}:Hameo(D^2,\partial D^2) \to \mathbb R$ to that of the vanishing of the basic phase function $f_{\underline{\mathbb F}}$, a Floer theoretic graph se…