Difference between revisions of "Table of contents"
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* [[Deligne-Mumford space]] (Nate-work-in-progress) | * [[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) | * [[Compactified Morse trajectory spaces]] (brief summary with references - could use extension) | ||
* [[Coherent orientations on the regularized moduli spaces]] arising from polyfold theory (TODO) | * [[Coherent orientations on the regularized moduli spaces]] arising from polyfold theory (TODO) |
Revision as of 13:01, 9 June 2017
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 (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 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)