Difference between revisions of "Table of contents"
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* the [[Cauchy-Riemann section]] as continuous map <math>\overline\partial_{J,Y}:\mathcal{X}(\underline{x})\to \mathcal{Y}_J(\underline{x})</math> (K-TODO) | * the [[Cauchy-Riemann section]] as continuous map <math>\overline\partial_{J,Y}:\mathcal{X}(\underline{x})\to \mathcal{Y}_J(\underline{x})</math> (K-TODO) | ||
** [[gluing construction]] for Hamiltonian perturbations (TODO) | ** [[gluing construction]] for Hamiltonian perturbations (TODO) | ||
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'''Analysis details:''' | '''Analysis details:''' | ||
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* the [[polyfold smooth structure]] on the [[ambient space]] <math>\mathcal{X} (\underline{x}) </math> (J-TODO) | * the [[polyfold smooth structure]] on the [[ambient space]] <math>\mathcal{X} (\underline{x}) </math> (J-TODO) | ||
* the [[polyfold bundle structure]] of the [[ambient bundle]] <math>\pi: \mathcal{Y}_J(\underline{x}) </math> (J-TODO) | * the [[polyfold bundle structure]] of the [[ambient bundle]] <math>\pi: \mathcal{Y}_J(\underline{x}) </math> (J-TODO) | ||
* the [[polyfold Fredholm property]] of the [[Cauchy-Riemann section]] <math>\overline\partial_{J,Y}:\mathcal{X}(\underline{x})\to \mathcal{Y}_J(\underline{x})</math> (J-TODO) | * the [[polyfold Fredholm property]] of the [[Cauchy-Riemann section]] <math>\overline\partial_{J,Y}:\mathcal{X}(\underline{x})\to \mathcal{Y}_J(\underline{x})</math> (J-TODO) | ||
| + | * proof that [[Gromov compactness implies properness]] of the [[Cauchy-Riemann section]] (TODO) | ||
Revision as of 15:49, 6 June 2017
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)
- 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)
- 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)
- gluing construction for Hamiltonian perturbations (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)
