# Download 4-Manifolds and Kirby Calculus (Graduate Studies in by András I. Stipsicz, Robert E. Gompf PDF

By András I. Stipsicz, Robert E. Gompf

The previous twenty years have introduced explosive progress in 4-manifold conception. Many books are at the moment showing that technique the subject from viewpoints similar to gauge idea or algebraic geometry. This quantity, besides the fact that, bargains an exposition from a topological viewpoint. It bridges the space to different disciplines and offers classical yet vital topological suggestions that experience now not formerly seemed within the literature. half I of the textual content offers the fundamentals of the idea on the second-year graduate point and provides an summary of present learn. half II is dedicated to an exposition of Kirby calculus, or handlebody concept on 4-manifolds. it really is either user-friendly and entire. half III bargains intensive a wide diversity of themes from present 4-manifold examine. themes contain branched coverings and the geography of complicated surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. purposes are featured, and there are over three hundred illustrations and various routines with options within the e-book.

**Read or Download 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics, Volume 20) PDF**

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**Example text**

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V S is S u Int S such If C that 2-sphere in a is called a C then i s a crumpled cube and if for each open set U K C V C U loop and any topological space each in K is a subset of C containing in V - K K Bd C, t h e n there is an is nullhomotopic in (See [13, p. 4. > O. A D' disk Let C be a crumpled cube in is called an and there exist null sequences (i) each D. (2) each D! (3) each D. [4) (S) Int D' - U. } 1 i=i D! if a disk in Bd C, and D N D' = Bd D = Bd D' is locally finite in is locally finite in is of diameter less than 1 Bd C - D; Int D'; e; Int D!