Difference between revisions of "Table of contents"
From Polyfolds.org
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* [[Brane structure]] (TODO) | * [[Brane structure]] (TODO) | ||
** [[Grading induced by brane structures]] (TODO) | ** [[Grading induced by brane structures]] (TODO) | ||
| + | * [[orientations of Cauchy-Riemann sections]] induced by brane structures (TODO) | ||
Geometry/Topology/Combinatorics details: | Geometry/Topology/Combinatorics details: | ||
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** [[glued surface]] (TODO - ? ref to part of Nate's ?) | ** [[glued surface]] (TODO - ? ref to part of Nate's ?) | ||
* [[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]] | + | * [[Coherent orientations on the regularized moduli spaces]] arising from polyfold theory (TODO) |
| + | * the polyfold [[ambient space]] <math>\mathcal{X} (\underline{x}) </math> as a topological space | ||
| + | * the polyfold [[ambient bundle]] <math>\pi: \mathcal{Y}_J(\underline{x}) </math> as continuous surjection between topological spaces | ||
| + | * the [[Cauchy-Riemann section]] as continuous map <math>\overline\partial_{J,Y}:\mathcal{X}(\underline{x})\to \mathcal{Y}_J(\underline{x})</math> | ||
| + | |||
Analysis details: | Analysis details: | ||
* [[gluing construction]] for Hamiltonian perturbations (TODO) | * [[gluing construction]] for Hamiltonian perturbations (TODO) | ||
* [[Gromov topology]] (TODO) | * [[Gromov topology]] (TODO) | ||
| + | * proof that [[Gromov compactness implies properness]] (TODO) | ||
Revision as of 16:41, 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 (TODO - ? ref to part of Nate's ?)
- 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 - the polyfold ambient bundle
as continuous surjection between topological spaces - the Cauchy-Riemann section as continuous map
Analysis details:
- gluing construction for Hamiltonian perturbations (TODO)
- Gromov topology (TODO)
- proof that Gromov compactness implies properness (TODO)
