Difference between revisions of "Table of contents"

Revision as of 19:31, 7 June 2017

Table of contents for Polyfold Constructions for Fukaya Categories

Construction overviews:

Algebra details:

Geometry/Topology/Combinatorics details:

Deligne-Mumford space (Nate-work-in-progress)
- Glued surface (N-TODO)
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 $\pi :{\mathcal {Y}}_{J}(\underline {x})$ as continuous surjection between topological spaces (K-TODO)
the Cauchy-Riemann section as continuous map (K-TODO)
- Gluing construction for Hamiltonian perturbations (TODO)

Analysis details:

the polyfold smooth structure on the ambient space ${\mathcal {X}}(\underline {x})$ (J-TODO)
the polyfold bundle structure of the ambient bundle $\pi :{\mathcal {Y}}_{J}(\underline {x})$ (J-TODO)
the polyfold Fredholm property of the Cauchy-Riemann section $\overline \partial _{{J,Y}}:{\mathcal {X}}(\underline {x})\to {\mathcal {Y}}_{J}(\underline {x})$ (J-TODO)
proof that Gromov compactness implies properness of the Cauchy-Riemann section (TODO)

@@ Line 6: / Line 6: @@
 * [[Moduli spaces of pseudoholomorphic polygons]]
-* [[Regularized moduli spaces]] (Katrin-work-in-progress)
+* [[Regularized moduli spaces]]
 * summary of resulting [[Floer chain complex]] (TODO)