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

By András I. Stipsicz, Robert E. Gompf

ISBN-10: 0821809946

ISBN-13: 9780821809945

The earlier 20 years have introduced explosive development in 4-manifold thought. Many books are at present showing that procedure the subject from viewpoints resembling gauge concept or algebraic geometry. This quantity, even though, deals an exposition from a topological standpoint. It bridges the space to different disciplines and provides classical yet very important topological thoughts that experience now not formerly seemed within the literature. half I of the textual content provides the fundamentals of the idea on the second-year graduate point and provides an summary of present examine. half II is dedicated to an exposition of Kirby calculus, or handlebody conception on 4-manifolds. it truly is either straight forward and finished. half III bargains intensive a large diversity of themes from present 4-manifold examine. themes comprise branched coverings and the geography of advanced surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. functions are featured, and there are over three hundred illustrations and various workouts with options within the publication.

Show description

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

Similar topology books

Download e-book for iPad: Hodge Theory of Projective Manifolds by Mark Andrea A De Cataldo

This ebook is a written-up and extended model of 8 lectures at the Hodge thought of projective manifolds. It assumes little or no historical past and goals at describing how the speculation turns into steadily richer and extra attractive as one specializes from Riemannian, to Kähler, to complicated projective manifolds.

Foundations of Symmetric Spaces of Measurable Functions: by Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. PDF

Key definitions and leads to symmetric areas, really Lp, Lorentz, Marcinkiewicz and Orlicz areas are emphasised during this textbook. A finished evaluation of the Lorentz, Marcinkiewicz and Orlicz areas is gifted according to innovations and result of symmetric areas. Scientists and researchers will locate the appliance of linear operators, ergodic concept, harmonic research and mathematical physics noteworthy and worthy.

Extra info for 4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics, Volume 20)

Example text

34 Let X be any space, and let ∗ ∈ X. Determine the mapping spaces map(S 0 , X) and map∗ (S 0 , X). In other words, give a complete description of these spaces in terms of X, and not including any mapping spaces. A special case of pointed mapping spaces that is very important is the set of pointed maps from S 1 to X; this particular mapping space is denoted Ω(X), and is called the loop space of X. 25, map∗ (X, Ω(Y )) ∼ = map∗ (S, Y ). for some pointed space S. Give an explicit description of the space S.

Every point x in the northern hemisphere is equivalent to exactly one point in the southern hemisphere. Another Description of CW Complexes. Each n-cell of a CW complex X has a corresponding map χ : Dn → X defined by the diagram Dn _ k Sn f  Xn ‘ k jn i /  k χ Dn+1  / Xn+1 This is called the characteristic map of the cell. 2 Jason Trowbridge’s idea.  / X. 8 Let X be a CW complex. , it is a homeomorphism onto its image. The image of χ is called an open n-cell of X. (b) Show that X is the union of the interiors of its cells (we interpret the interior of a 0-cell to be the cell itself), and that those open cells are pairwise disjoint.

Alternatively, construct a natural isomorphism between the functors morC ( ? , P ) and morC ( ? , Q). Domains and Targets. Colimits C are defined in such a way that we are given information about morphisms C → Z; so colimits are domain-type constructions. Dually, limits are defined so that we have information about morphims Z → L; and hence limits are target-type constructions. 13 Show that the colimit of the empty diagram ∅ → C is an initial object in C. Show that the limit of the identity idC is an initial object in C.

Download PDF sample

4-Manifolds and Kirby Calculus (Graduate Studies in Mathematics, Volume 20) by András I. Stipsicz, Robert E. Gompf


by Brian
4.1

Rated 4.96 of 5 – based on 17 votes