Table of contents

Table of contents for Polyfold Constructions for Fukaya Categories

Construction overviews:

• Moduli spaces of pseudoholomorphic polygons
• Regularized moduli spaces (Katrin-work-in-progress)
• summary of resulting Floer chain complex (TODO)

Algebra details:

• Novikov ring (TODO)
• Brane structure (TODO)
  • Grading induced by brane structures (TODO)
• orientations of Cauchy-Riemann sections induced by brane structures (TODO)

Geometry/Topology/Combinatorics details:

• Deligne-Mumford space (Nate-work-in-progress)
  • glued surface (TODO - ? ref to part of Nate's ?)
• compactified Morse trajectory spaces (brief summary with references - could use extension)
• Coherent orientations on the regularized moduli spaces arising from polyfold theory (TODO)
• the polyfold ambient space ${\mathcal {X}}(\underline {x})$ as a topological space
• the polyfold ambient bundle $\pi :{\mathcal {Y}}_{J}(\underline {x})$ as continuous surjection between topological spaces
• the Cauchy-Riemann section as continuous map $\overline \partial _{{J,Y}}:{\mathcal {X}}(\underline {x})\to {\mathcal {Y}}_{J}(\underline {x})$

Analysis details:

• gluing construction for Hamiltonian perturbations (TODO)
• Gromov topology (TODO)
• proof that Gromov compactness implies properness (TODO)