An Introduction to Compactness Results in Symplectic Field by Casim Abbas

By Casim Abbas

This booklet presents an advent to symplectic box idea, a brand new and demanding topic that is presently being built. the place to begin of this concept are compactness effects for holomorphic curves tested within the final decade. the writer offers a scientific creation supplying loads of heritage fabric, a lot of that is scattered through the literature. because the content material grew out of lectures given via the writer, the most objective is to supply an access aspect into symplectic box conception for non-specialists and for graduate scholars. Extensions of sure compactness effects, that are believed to be precise by way of the experts yet haven't but been released within the literature intimately, refill the scope of this monograph.

Show description

Read or Download An Introduction to Compactness Results in Symplectic Field Theory PDF

Similar topology books

Tel Aviv Topology Conference: Rothenberg Festschrif : International Conference on Topology, June 1-5, 1998 Tel Aviv (Contemporary Mathematics)

This quantity provides the court cases of the Tel Aviv foreign Topology convention held throughout the designated Topology software at Tel Aviv college. The booklet is devoted to Professor Mel Rothenberg at the celebration of his sixty fifth birthday. His contributions to topology are good known---from the early paintings on triangulations to various papers on transformation teams and on geometric and analytic elements of torsion conception.

Topology, 2/E

For a senior undergraduate or first 12 months graduate-level path in advent to Topology. acceptable for a one-semester path on either normal and algebraic topology or separate classes treating every one subject separately.
This textual content is designed to supply teachers with a handy unmarried textual content source for bridging among normal and algebraic topology classes. separate, designated sections (one on common, aspect set topology, the opposite on algebraic topology) are every one compatible for a one-semester direction and are dependent round the related set of easy, middle subject matters. non-compulsory, self sufficient issues and functions will be studied and built extensive looking on path wishes and preferences.

Table of Contents

I. normal TOPOLOGY.
1. Set concept and Logic.

2. Topological areas and non-stop Functions.

three. Connectedness and Compactness.

four. Countability and Separation Axioms.

five. The Tychonoff Theorem.

6. Metrization Theorems and Paracompactness.

7. entire Metric areas and serve as Spaces.

eight. Baire areas and size Theory.

nine. the basic Group.

10. Separation Theorems within the Plane.

11. The Seifert-van Kampen Theorem.

12. type of Surfaces.

13. type of overlaying Spaces.

14. purposes to team Theory.


Surface Topology

This up-to-date and revised version of a generally acclaimed and winning textual content for undergraduates examines topology of modern compact surfaces during the improvement of straightforward rules in aircraft geometry. Containing over 171 diagrams, the procedure permits an easy therapy of its topic quarter. it truly is quite beautiful for its wealth of purposes and diversity of interactions with branches of arithmetic, associated with floor topology, graph idea, staff concept, vector box thought, and airplane Euclidean and non-Euclidean geometry.

Geometry of polynomials

In the course of the years because the first variation of this famous monograph seemed, the topic (the geometry of the zeros of a fancy polynomial) has persisted to exhibit an identical striking energy because it did within the first a hundred and fifty years of its background, starting with the contributions of Cauchy and Gauss.

Extra info for An Introduction to Compactness Results in Symplectic Field Theory

Example text

We will combine these techniques with the results of Chapter 3 to show that, in fact, Hk (r*J is independent of g when g » k. Our starting point is once again the Riemann surface E* r of genus g with r boundary components and s punctures. £s and fix the punctures individually. 4 Computing the Cohomology of Mapping Class Groups between r* r and 39 T^'. Consider the following maps $ r > 2, * : r>2, n: r > 2, which we define as follows. For Vf, sew a pair of pants (a copy of the surface So 3 ) to the regular surface E* r along two components of its boundary.

2. According to Fenchel and Nielsen's work [1, 2], almost all hyperbolic surfaces (of finite topological type) can be obtained in this way. It is easy to see why: the parameters for the gluing are global coordinates for Teichmiiller space. To construct a surface of genus g requires 2g — 2 pairs of pants (the Euler characteristic for a pair of pants is —1). Each pair of pants has three boundaries and as such, they can be identified in pairs. There are three times | (2g — 2) gluing sites. At each site, there are two parameters, namely li and T;.

2); namely given the tangent vector fi € H (X), we can write Re(d/ c (/x)) = - / n0c. 3) 7T JX There is more to this. 4) A few comments are in order. 4). Here is how. Note that {C;} is a partition of S s giving the Fenchel-Nielsen coordinates {T,,/,}, as shown above. Thus, the twist vector fields tc{ are just the coordinate vector field g^-. The duality formula implies that u>wp is invariant under any twist flow. Putting this together with the fact that the coordinate vector fields {§7-, -gf} commute, one observes that the coefficients of LJWP in the basis {(ir,- A drj, dl{ A dr^ dl{ A dlf\ are independent of 77.

Download PDF sample

Rated 4.83 of 5 – based on 47 votes