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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]

• Lecture series on Polyfolds (H.Hofer, 2012 at IAS) [15], [16], [17], [18], [19], [20], [21], [22]

• 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 II: https://arxiv.org/abs/0705.1310 (H.Hofer, K.Wysocki, E.Zehnder, 2007) [30]

• 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]

• Fredholm notions in scale calculus and Hamiltonian Floer theory (K.Wehrheim, 2012&2016) [35]

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