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== Content Ideas ==
 
== Content Ideas ==
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* links to polyfold talks .. IHES .. IAS
 
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* annotated list of references
 
 
* space for conference/workshop announcements - such as SFT 9 in Augsburg
 
* space for conference/workshop announcements - such as SFT 9 in Augsburg
 
* ?? rather than Katrin (eventually) whipping up a separate polyfold lab page, maybe make a list of "polyfold people" with pictures and links to their personal websites/papers, space to state research interests ("contact me if ... ") .. include Wysocki memorial
 
* ?? rather than Katrin (eventually) whipping up a separate polyfold lab page, maybe make a list of "polyfold people" with pictures and links to their personal websites/papers, space to state research interests ("contact me if ... ") .. include Wysocki memorial
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* Transversality questions and polyfold structures for holomorphic disks (K.Wehrheim, 2009 at MSRI) [https://www.youtube.com/watch?v=4kgiFIkS-f0&list=PLXjpiiAr8QGJODAieckuuzks6fuRAKKLB&index=20]
 
* Transversality questions and polyfold structures for holomorphic disks (K.Wehrheim, 2009 at MSRI) [https://www.youtube.com/watch?v=4kgiFIkS-f0&list=PLXjpiiAr8QGJODAieckuuzks6fuRAKKLB&index=20]
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== Surveys and Textbooks on Polyfold Theory ==
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* Polyfold and Fredholm Theory I: Basic Theory in M-Polyfolds (H.Hofer, K.Wysocki, E.Zehnder, 2014) [https://arxiv.org/abs/1407.3185]
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* Polyfolds And A General Fredholm Theory (H.Hofer, 2008&2014) [https://arxiv.org/abs/1412.4255]
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* Polyfolds: A First and Second Look (O.Fabert, J.Fish, R.Golovko, K.Wehrheim, 2012)  [https://arxiv.org/abs/1210.6670]
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* A General Fredholm Theory and Applications (H.Hofer, 2005) [https://arxiv.org/abs/math/0509366]
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== Papers on abstract Polyfold Theory ==
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* A General Fredholm Theory I: A Splicing-Based Differential Geometry (H.Hofer, K.Wysocki, E.Zehnder, 2006) [https://arxiv.org/abs/math/0612604]
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*  A General Fredholm Theory II: https://arxiv.org/abs/0705.1310 (H.Hofer, K.Wysocki, E.Zehnder, 2007) [https://arxiv.org/abs/0705.1310]
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* A General Fredholm Theory III: Fredholm Functors and Polyfolds (H.Hofer, K.Wysocki, E.Zehnder, 2008) [https://arxiv.org/abs/0810.0736]
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* Integration Theory for Zero Sets of Polyfold Fredholm Sections (H.Hofer, K.Wysocki, E.Zehnder, 2007) [https://arxiv.org/abs/0711.0781]
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* Sc-Smoothness, Retractions and New Models for Smooth Spaces (H.Hofer, K.Wysocki, E.Zehnder, 2010) [https://arxiv.org/abs/1002.3381]
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== Papers on Polyfold Applications ==
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* Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory (H.Hofer, K.Wysocki, E.Zehnder, 2011) [https://arxiv.org/abs/1107.2097]
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== Getting started ==
 
== Getting started ==

Revision as of 18:17, 19 May 2017

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Content Ideas

  • space for conference/workshop announcements - such as SFT 9 in Augsburg
  •  ?? rather than Katrin (eventually) whipping up a separate polyfold lab page, maybe make a list of "polyfold people" with pictures and links to their personal websites/papers, space to state research interests ("contact me if ... ") .. include Wysocki memorial
  • Helmut was talking about making his own wiki out of "the book" ... so eventually link there (or have a separate part) ... in any case, we'll need to clearly separate rigorous presentation (parts of the book etc) from Fukaya-category work in progress
  • Fukaya category resources

Testing

Next, when studying differential equations we often work with the following subsets of {\mathcal {F}}[0,L].

{\mathcal {C}}[0,L]=\{f\in {\mathcal {F}}[0,L]\,|\,f\;{\text{continuous}}\} is the set of functions f:[0,L]\to \mathbb{R} that are continuous.

{\mathcal {C}}^{\infty }[0,L]=\{f\in {\mathcal {F}}[0,L]\,|\,f\;{\text{smooth}}\} is the set of functions f:[0,L]\to \mathbb{R} that are smooth. That is, all derivatives of f are required to be continuous.


OK, I had to replace all the abbreviations (it doesn't parse \def ) and then replace all $ by < math > when copying from a latex file of mine ... and I doubt it will take definition / theorem / ... environments ... so copying from tex files seems unwise, otherwise happy!

Videos of talks on polyfolds

  • 2015 Summer School on Moduli Problems in Symplectic Geometry playlist [1], in particular series by J.Fish, K.Wehrheim [2], [3], [4], [5], [6]; discussions with N.Bottman [7], [8]; H.Hofer on construction of SFT polyfolds [9], [10], [11], [12], [13]
  • Introduction to Polyfolds (K.Wehrheim, 2012 at IAS) [14]
  • An M-polyfold relevant to Morse theory (P.Albers, 2012 at IAS) [23]
  • Transversality questions and polyfold structures for holomorphic disks (K.Wehrheim, 2009 at MSRI) [24]

Surveys and Textbooks on Polyfold Theory

  • Polyfold and Fredholm Theory I: Basic Theory in M-Polyfolds (H.Hofer, K.Wysocki, E.Zehnder, 2014) [25]
  • Polyfolds And A General Fredholm Theory (H.Hofer, 2008&2014) [26]
  • Polyfolds: A First and Second Look (O.Fabert, J.Fish, R.Golovko, K.Wehrheim, 2012) [27]
  • A General Fredholm Theory and Applications (H.Hofer, 2005) [28]

Papers on abstract Polyfold Theory

  • A General Fredholm Theory I: A Splicing-Based Differential Geometry (H.Hofer, K.Wysocki, E.Zehnder, 2006) [29]
  • A General Fredholm Theory III: Fredholm Functors and Polyfolds (H.Hofer, K.Wysocki, E.Zehnder, 2008) [31]
  • Integration Theory for Zero Sets of Polyfold Fredholm Sections (H.Hofer, K.Wysocki, E.Zehnder, 2007) [32]
  • Sc-Smoothness, Retractions and New Models for Smooth Spaces (H.Hofer, K.Wysocki, E.Zehnder, 2010) [33]


Papers on Polyfold Applications

  • Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory (H.Hofer, K.Wysocki, E.Zehnder, 2011) [34]



Getting started

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