# Table of contents

From Polyfolds.org

Revision as of 12:02, 9 June 2017 by Natebottman (Talk | contribs)

**Table of contents** for Polyfold Constructions for Fukaya Categories

**Construction overviews:**

- Moduli spaces of pseudoholomorphic polygons
- Regularized moduli spaces
- summary of resulting Floer chain complex (TODO)

**Algebra details:**

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

**Geometry/Topology/Combinatorics details:**

- Deligne-Mumford space (N-work-in-progress)
- glued surface (N-work in progress -- and need to synchronize with reference to this in [expansion of expansion in point 7] and Gluing construction for Hamiltonians )

- 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 as a topological space (K-TODO)
- Gromov topology (K-TODO)

- the polyfold ambient bundle as continuous surjection between topological spaces (K-TODO)
- the Cauchy-Riemann section as continuous map (K-TODO)

**Analysis details:**

- the polyfold smooth structure on the ambient space (J-TODO)
- the polyfold bundle structure of the ambient bundle (J-TODO)
- the polyfold Fredholm property of the Cauchy-Riemann section (J-TODO)
- proof that Gromov compactness implies properness of the Cauchy-Riemann section (TODO)