相关论文: Pseudoholomorphic Strips in Symplectisations II: F…
This survey wants to give a short introduction to the transversality problem in symplectic field theory and motivate to approach it using the new Fredholm theory by Hofer, Wysocki and Zehnder. With this it should serve as a lead-in for the…
See hep-ph/0304045
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and…
This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).
This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an…
This is a reference volume on polyfold and Fredholm theory.
This paper is part of a larger program, the investigation of the Chord Problem in three dimensional contact geometry. The main tool will be pseudoholomorphic strips in the symplectisation of a three dimensional contact manifold with two…
In this paper we study pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudoholomorphic curve with brake symmetry and the corresponding moduli space. Then we get the virtual…
Withdrawn by author due to copyright transfer. See: http://www3.interscience.wiley.com/cgi-bin/abstract/116836954/ABSTRACT
The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work of Gromov, McDuff and Taubes on…
The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the…
Withdrawal Notice: SWJPAM does not allow articles it publishes to appear on archives. An updated version of this article along with new results, can be found at the author's web page: www.math.psu.edu/horwitz/papers.html
This paper gives methods for understanding invariants of symplectic quotients. The symplectic quotients considered here are compact symplectic manifolds (or more generally orbifolds), which arise as the symplectic quotients of a symplectic…
A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline arrangement. We study the corresponding graph realization problem and properties of pseudoline arrangement graphs. In the first part, we give…
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
These are (heavily revised) notes from lectures given at the AMS Algebraic Geometry meeting in Seattle, 2005. The main topic is symplectic homology seen from the point of view of Lefschetz fibrations. Most of the content is speculative, but…
Correction to The Annals of Probability 21 (1993) 554--580 [http://projecteuclid.org/euclid.aop/1176989415]
Doubly periodic tangles (DP tangles) are configurations of curves embedded in the thickened plane, invariant under translations in two transversal directions. In this paper we extend the classical theory of DP tangles by introducing the…