Regularization of moduli spaces of pseudholomorphic curves

 

a collection of literature that the course may refer to

Pseudoholomorphic Curves - general expositions

Audin-Damian, Morse Theory and Floer Homology, Springer

McDuff-Salamon, J-holomorphic Curves and Symplectic Topology, AMS

McDuff-Salamon, J-Holomorphic Curves and Quantum Cohomology, AMS, 1995

Salamon, Lectures on Floer homology

Schwarz, Cohomology Operations from Cobordisms in Floer Homology, Thesis, 1995

Regularization Philosophy

Fabert-Fish-Golovko-Wehrheim, Polyfolds: A first and second look, preprint 2013

Hofer:
A General Fredholm Theory and Applications, 2005
Polyfolds And A General Fredholm Theory, 2008

McDuff-Wehrheim, Sections 2,3 of Smooth Kuranishi atlases with trivial isotropy, preprint 2013

Regularization by finite dimensional reduction

Fukaya-Ono, Arnold conjecture and Gromov-Witten invariant, Topology 1999

Fukaya-Oh-Ohta-Ono, Lagrangian intersection Floer theory: anomaly and obstruction, Part II, AMS, 2009

Joyce, Kuranishi homology and Kuranishi cohomology, preprint 2007

McDuff-Wehrheim, Smooth Kuranishi atlases with trivial isotropy, preprint 2013

Regularization by stabilization and Euler class

Li-Tian, Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds, in Topics in symplectic 4-manifolds, Int.Press 1998

Liu-Tian, Floer homology and Arnold conjecture, J. Differential Geom.1998

Siebert, Gromov-Witten invariants of general symplectic manifolds, preprint 1996

Regularization by Polyfold Fredholm sections

Hofer-Wysocki-Zehnder:
A General Fredholm Theory I: A Splicing-Based Differential Geometry
A General Fredholm Theory II: Implicit Function Theorems
A General Fredholm Theory III: Fredholm Functors and Polyfolds
Sc-Smoothness, Retractions and New Models for Smooth Spaces
Integration Theory for Zero Sets of Polyfold Fredholm Sections
Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory

Wehrheim, Fredholm notions in scale calculus and Hamiltonian Floer theory

Various Background

McDuff, Groupoids, branched manifolds and multisections, J. Symplectic Geom. 2006