Difference between revisions of "Table of contents"

Revision as of 12:01, 9 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 .. or replace 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 $\pi :{\mathcal {Y}}_{J}(\underline {x})$ as continuous surjection between topological spaces (K-TODO)
the Cauchy-Riemann section as continuous map (K-TODO)
- Gluing construction for Hamiltonians (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 21: / Line 21: @@
 * [[Deligne-Mumford space]] (Nate-work-in-progress)
-** [[Deligne-Mumford space#Gluing and the definition of the topology]] (N-TODO .. or replace reference to this in [[http://www.polyfolds.org/index.php?title=Moduli_spaces_of_pseudoholomorphic_polygons#General_moduli_space_of_pseudoholomorphic_polygons  expansion of expansion in point 7]] and  [[Gluing construction for Hamiltonians]] )
+** [[Deligne-Mumford space#Gluing and the definition of the topology|glued surface]] (N-TODO .. or replace reference to this in [[http://www.polyfolds.org/index.php?title=Moduli_spaces_of_pseudoholomorphic_polygons#General_moduli_space_of_pseudoholomorphic_polygons  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)