Fredholm Theory for Pseudoholomorphic Curves with Brake Symmetry

Iteration Formulae for Brake Orbit and Index Inequalities for Real Pseudoholomorphic Curves

I give precise iteration formulae for brake orbit in dimension 3 and use these formulae to get some index inequalities for moduli spaces of Real pseudoholomorphic Curves, which are important to establish Real embedded contact homology and Real cylindrical contact homology in dimension 3.

Pseudoholomorphic Strips in Symplectisations II: Fredholm theory and Transversality

See http://www.math.msu.edu/~abbas or Wiley preprint server.

Polyfold基本类与全局结构化多值扰动

Polyfold fundamental classes and globally structured multivalued perturbations

针对Hofer等人提出的polyfold Fredholm截面框架提取拓扑信息方法繁琐的问题，本文构建了具备全局结构的有限维多值扰动空间，可在模空间无形式边界时清晰定义其有理Čech基本类。

Counterexamples in Scale Calculus

We construct counterexamples to classical calculus facts such as the Inverse and Implicit Function Theorems in Scale Calculus -- a generalization of Multivariable Calculus to infinite dimensional vector spaces in which the reparameterization maps relevant to Symplectic Geometry are smooth. Scale Calculus is a cornerstone of Polyfold Theory, which was introduced by Hofer-Wysocki-Zehnder as a broadly applicable tool for regularizing moduli spaces of pseudoholomorphic curves. We show how the novel nonlinear scale-Fredholm notion in Polyfold Theory overcomes the lack of Implicit Function Theorems,…