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

By András I. Stipsicz, Robert E. Gompf

The prior 20 years have introduced explosive progress in 4-manifold concept. Many books are presently showing that procedure the subject from viewpoints similar to gauge concept or algebraic geometry. This quantity, despite the fact that, bargains an exposition from a topological viewpoint. It bridges the space to different disciplines and provides classical yet vital topological strategies that experience no longer 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 outline of present learn. half II is dedicated to an exposition of Kirby calculus, or handlebody idea on 4-manifolds. it really is either uncomplicated and accomplished. half III bargains extensive a vast diversity of issues from present 4-manifold learn. subject matters comprise branched coverings and the geography of complicated surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. functions are featured, and there are over three hundred illustrations and diverse workouts with suggestions within the booklet.

Show description

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

Similar topology books

Infinite words : automata, semigroups, logic and games

Countless phrases is a crucial idea in either arithmetic and machine Sciences. Many new advancements were made within the box, inspired through its program to difficulties in desktop technological know-how. endless phrases is the 1st handbook dedicated to this subject. countless phrases explores all facets of the speculation, together with Automata, Semigroups, Topology, video games, good judgment, Bi-infinite phrases, endless timber and Finite phrases.

Topological Vector Spaces

The current booklet is meant to be a scientific textual content on topological vector areas and presupposes familiarity with the weather of common topology and linear algebra. the writer has came across it pointless to rederive those effects, considering the fact that they're both uncomplicated for plenty of different components of arithmetic, and each starting graduate scholar is probably going to have made their acquaintance.

Hamiltonian Dynamics and Celestial Mechanics: A Joint Summer Research Conference on Hamiltonian Dynamics and Celestial Mechanics June 25-29, 1995 Seattle, Washington

This booklet comprises chosen papers from the AMS-IMS-SIAM Joint summer season study convention on Hamiltonian platforms and Celestial Mechanics held in Seattle in June 1995.

The symbiotic courting of those subject matters creates a traditional blend for a convention on dynamics. subject matters lined contain twist maps, the Aubrey-Mather idea, Arnold diffusion, qualitative and topological reports of platforms, and variational tools, in addition to particular subject matters resembling Melnikov's process and the singularity houses of specific systems.

As one of many few books that addresses either Hamiltonian platforms and celestial mechanics, this quantity bargains emphasis on new matters and unsolved difficulties. a number of the papers supply new effects, but the editors purposely incorporated a few exploratory papers in response to numerical computations, a piece on unsolved difficulties, and papers that pose conjectures whereas constructing what's known.


Open examine problems
Papers on crucial configurations

Readership: Graduate scholars, examine mathematicians, and physicists attracted to dynamical platforms, Hamiltonian platforms, celestial mechanics, and/or mathematical astronomy.

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

Sample text

Let us show that there exists a Moscow group G such that X x G is not a PT-group. In fact, G can be selected to be a topological group of countable pseudocharacter. 7 are closed, and the closures of elements of r/in # X do not cover # X . Note, that # X is, in this case, the product of w~ copies of D = {0, 1}. 7. Clearly, G is a topological group. It is also obvious that G is Ra~ov complete. 7 such that U7 is dense in X. For each P E "7 and each positive n E w, the set Up, n of all f E G such that If(z)] < 1In for every z E P is open in G and contains the zerofunction 0 on X which is the neutral element of G.

In this case, the Bohr topology on G coincides with the weak topology generated by the family of all continuous characters on G, and G with this topology is denoted by G +. In particular, all locally compact Abelian groups belong to the class of MAP groups. The Bohr topology of locally compact Abelian groups was studied in many articles, some of them quite recent. 3. THEOREM.

The topological group (7* so obtained is a P-space. Then G* is not a Moscow space. Therefore, G* may be a candidate for being a non-PT-group. However, the solution to the PT-problem in ARHANGEL'SKII [2000a] presented below is based on a different idea. A topological group (7 is called Ro-bounded provided that for each neighborhood V of the neutral element there exists a countable subset A of (7 such that A V = G. Tka~enko has shown that every R-factorizable group is Ro-bounded and that not every lqo-bounded group is R-factorizable (see TKAt~ENKO [1991b]).

Download PDF sample

Rated 5.00 of 5 – based on 27 votes