For those genuinely interested in understanding the proof of the 4 dimensional poincare conjecture, and for those who need a more geometric, intuitive view of some of the main results in topological 4 manifolds, rather than one based on the heavy machinery of algebraic topology, this book is an excellent beginning. Many interesting manifolds admit such decompositions and kirbys techniques have led to a deeper understanding of a number of these. All known 4manifolds invariants cannot distinguish a possible counterexample to the smooth 4dimensional poincare conjecture from the standard 4sphere. Aug 01, 2003 in this article we continue to investigate exotic smooth structures of 4manifolds studied in forum math.
Lectures on the topology of 3 manifolds by giuseppedurr issuu. Department of mathematics, university of texas, austin. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. Since the early 1980s, there has been an explosive growth in 4manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. In this paper, we construct a family of symplectic 4manifolds with positive. Kirby s theorem gives the answer when the manifold is s3, and fenn and rourke extended it to the case of any closed orientable. Jun 18, 20 we describe rules for building 2d theories labeled by 4 manifolds. Gompf and andras stipsiczs 4manifolds and kirby calculus. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. Download book 4 manifolds and kirby calculus graduate studies in mathematics in pdf format.
Kirby s theorem is an important method for constructing invariants of 3 manifolds. With the help of open books one can likewise represent at least some 5manifolds by 3dimensional diagrams, and contact geometry can be used to reduce these to drawings in the 2plane. In addition to this current volume 1965, he is also well known for his introductory but rigorous textbook calculus 1967, 4th ed. Graduate studies in mathematics publication year 1999. Acrobat reader 4manifolds and kirby calculus full text information 4manifolds and kirby calculus.
An extended set of diagrams and moves are used for describing 4manifolds. Lectures on the topology of 3manifolds an introduction to. Exotic smooth structures on 4manifolds, ii sciencedirect. And now i have another simple question that is more linguistic in nature. It is well known that every closed oriented 3manifold can be obtained from s3 by surgery along a framed link 8, 11. This allows an extension of the kirby calculus to rational surgeries. Kirby calculus, a method for describing 3manifolds and smooth 4manifolds by surgery. Show that the manifold w in figure 8 is a contractible manifold, and by sugeries in its interior corresponding to zero and dot. Suppose there are two framed links in a compact, connected 3manifold possibly with boundary, or nonorientable such that the associated 3manifolds obtained by surgery are homeomorphic relative to their common boundary, if there is one.
Kirby calculus for nullhomologous framed links in 3manifolds. We show how to construct a kirby diagram for a large class of finite volume hyperbolic 4manifolds constructed by j. A list of recommended books in topology cornell university. Lefschetz fibrations of 4dimensional manifolds terry fuller department of mathematics california state university, northridge. The groundbreaking results of donaldson on lefschetz fibrations and giroux on open book decompositions now allow one to incorporate analytic structures into these diagrams. The manifolds in question are obtained by surgery on loops. Most of the proofs are new or are returbishings of post proofs. The methods we use are modified surgery of kreck \citekreck and kirby calculus. Surgery on contact 3manifolds and stein surfaces burak. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable firstyear calculus course one which at least mentions the least upper bound sup and greatest lower bound inf of a set of real numbers. Part i of the text presents the basics of the theory at the secondyear graduate level and offers an overview of current research.
Kirby diagrams and the ratcliffetschantz hyperbolic 4. Jun 20, 20 issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. In this article we continue to investigate exotic smooth structures of 4manifolds studied in forum math. Download direct 4manifolds and kirby calculus graduate studies in mathematics.
May 31, 2015 so this is beginning to feel like the beginning of the 4th movement of beethovens ninth. Scorpans wild world of 4manifolds is to my knowledge a unique book in that it covers extensively just about everything that one would need to know to study 4manifold topology, both the topological i. In mathematics, the kirby calculus in geometric topology, named after robion kirby, is a method for modifying framed links in the 3sphere using a finite set of moves, the kirby moves. European mathematical society newsletter 4 manifolds and kirby calculus invites the reader to think positively, if you ever find yourself in a bad condition, remember that even if you can lose everything else, your work, your property, your money and even your health knowledge can never be removed from you. Freedman implies that the homeomorphism type of the manifold only depends on this intersection form, and on a z2z invariant called the kirby siebenmann invariant, and moreover that every combination of. Is there a good notation for kirby diagrams for manifolds with boundaries, i. One of the largest censuses of finite volume hyperbolic 4 manifolds was constructed by j. This book presents the classical theorems about simply connected smooth 4manifolds. Zalerts allow you to be notified by email about the availability of new books according to your search query. In mathematics, 4manifold is a 4dimensional topological manifold.
Part ii is devoted to an exposition of kirby calculus, or handlebody theory on 4 manifolds. More generally, we also show the existence of 4 manifolds without gompf nuclei nn. You did not read calculus of a single variable 7th edition answers epub, then you will suffer huge losses. The book covers some classical material, such as heegaard splittings, dehn surgery, and invariants of knots and links. In what follows, unless otherwise speci ed, we will suppose all the manifolds are smooth and oriented.
Gompf, university of texas, austin, austin, tx and andras i. Download citation kirby diagrams and the ratcliffetschantz hyperbolic 4manifolds we show how to construct a kirby diagram for a large class of finite volume hyperbolic 4manifolds. The proofs rely on the connection between the smooth topology and the seibergwitten basic classes of a given 4 dimensional manifold m. You can read online 4 manifolds and kirby calculus graduate studies in mathematics here in pdf, epub, mobi or docx formats.
On kirby calculus for nullhomotopic framed links in 3manifolds. Di eomorphism between oriented manifolds will be assumed to be orientation preserving. Kirby has devised a calculus of framed links for the study of such manifolds 11. An extended set of diagrams and moves are used for describing 4 manifolds. Realizing 4manifolds as achiral lefschetz fibrations. Kirby calculus for nullhomologous framed links in 3manifolds kazuo habiro rims, kyoto university in this talk, i plan to explain our recent results joint with t. Easily share your publications and get them in front of issuus. Using fourdimensional cerf theory, he proved that if m and n are 3manifolds. Stipsicz american mathematical society providence, rhode island graduate studies in mathematics. The mid1990s saw a number of developments which made symplectic 4 manifolds natural candidates to be the building blocks of all smooth 4 manifolds.
Part iii offers in depth a broad range of topics from current 4 manifold research. Calculus of a single variable 9th edition pdf pdf book. A framed link l in s 3 is a finite, disjoint collection of smoothly imbedded. Read online 4manifolds and kirby calculus book pdf free download link book now. A search query can be a title of the book, a name of the author, isbn or anything else. Everyone will get a lot of knowledge by reading this book. Stipsicz, 4manifolds and kirby calculus, in graduate studies in. In particular, we point out that the gluing measure.
Part iii offers in depth a broad range of topics from current 4manifold research. Foundational essays on topological manifolds, smoothings, and triangulations pdf. The homotopy type of a simply connected compact 4manifold only depends on the intersection form on the middle dimensional homology. A guide to the classification of manifolds exotic smoothness and. Download 4 manifolds and kirby calculus or read online here in pdf or epub. The book should be useful to beginning researchers in 4manifolds.
A framed link in the 3sphere encodes instructions for attaching 2handles to the 4ball. Gompf showed that a basic cut and paste operation, a symplectic normal sum, could be performed on symplectic. Please click button to get 4 manifolds and kirby calculus book now. A framed link in the 3sphere encodes instructions for attaching 2handles to the 4 ball.
Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase. Buy 4manifolds and kirby calculus graduate studies in mathematics on. Download pdf 4 manifolds and kirby calculus graduate. Kaplan received 17 hnuary 1979 a usual starting point in studying a smooth, compact, simply connected 4manifold w4 is to. It would be wonderful for a lot of things that you need here. A calculus for framed links in s 3 robion kirby university of california, department of mathematics, berkeley, ca. Get your kindle here, or download a free kindle reading app. All 3manifolds are the boundary of exotic 4manifolds.
All books are in clear copy here, and all files are secure so dont worry about it. This content was uploaded by our users and we assume good faith they have the permission to share this book. In mathematics, a 4manifold is a 4dimensional topological manifold. There are also various tricks to modify surgery diagrams. Download 4manifolds and kirby calculus book pdf free download link or read online here in pdf. By analogy, one can draw 2dimensional pictures of 3manifolds heegaard diagrams, and 3dimensional pictures of 4manifolds kirby diagrams.
It then proceeds through the kirby calculus and rohlins theorem to cassons invariant and its applications, and concludes with a brief overview of recent developments. In this paper we construct explicit examples of both closed and noncompact finite volume hyperbolic manifolds which provide counterexamples to the conjecture that the corank of a 3manifold group also known as the cut number is bounded below by onethird the first betti number. Calculus of a single variable 7th edition answers epub. Handle decomposition handle decompositions provide a way to better. Since the worldsheet scft of a heterotic string is a prominent member of this class of 2d n 0,2 theories we shall call it class h in what follows. American mathematical society, providence, ri, 1999.
Moreover, much of the material is substantially repeated from earlier study and it proceeds at a slow pace with extensive practice and. Robion cromwell kirby born february 25, 1938 is a professor of mathematics at the. The l invariant, defined in this paper, can do so, for if it vanishes on a homotopy 4sphere x, then x must be diffeomorphic to the 4sphere. Kirby, a calculus for framed links inventiones math. In this paper, we prove a variant of kirby s theorem for nullhomologous framed links in a 3manifold. They construct a total of 1171 distinct isometry classes of finite volume. Manifolds,lie algebra, lie groups and exterior algebra. Kirby diagrams and the ratcliffetschantz hyperbolic 4manifolds. Are there kirby diagrams for manifolds with boundaries.
Over the last fifteen years, the geometrical and topological equipment of the idea of manifolds have assumed a relevant position within the such a lot complicated parts of natural and utilized arithmetic in addition to theoretical physics. We show how to construct broken, achiral lefschetz fibrations on arbitrary smooth, closed, oriented 4manifolds. The focus in this paper is to explicitly construct kirby diagrams for a certain collection of finite volume hyperbolic 4 manifolds. Michael spivak brandeis university calculus on manifolds a modern approach to classical theorems of advanced calculus addisonwesley publishing company the advanced book program reading, massachusetts menlo park, california new york don mills, ontario wokingham, england amsterdam bonn. Examples of 4manifolds without gompf nuclei springerlink. Manifold intelligence a research project at the university of texas at austin is at the forefront of a study of the complex. Now the ordinary calculus of r n can be patched together via the transition functions to allow one to do calculus on all of m. Instantons and the topology of 4manifolds ronald j. Part ii is devoted to an exposition of kirby calculus, or handlebody theory on 4manifolds.
This book offers an exposition of the subject from the topological point of view. In this talk i will introduce the topic and discuss the aim of the seminar. We show that the 4 manifold x2,2,2 defined below does not contain the gompf nucleus n2. There exist some topological 4manifolds which admit no smooth structure and even if there exists a smooth structure it need not be unique i. We study a class of 2d n 0,2 theories tm4 labeled by 4manifolds with boundary that enjoys all the standard operations on 4manifolds, such as cutting, gluing, and the kirby moves 1. Widmer on kirby calculus for framed links in 3manifolds 5, 6. This site is like a library, you could find million book here by using search box in the widget. These are generalizations of lefschetz fibrations over the 2sphere, where we allow lefschetz singularities with the nonstandard orientation as well as circles of singularities corresponding to round 1handles. A smooth 4manifold is a 4manifold with a smooth structure. One suggestion for the 4 dimensional case might be drawing a circle with one half in a different colour for 2handles with boundary. We prove a similar result which states that two smooth closed 4 manifolds satisfying certain properties are stably diffeomorphic if and only if their signatures agree.
477 1462 191 1461 482 1267 1434 183 1243 494 428 950 985 1480 363 728 1222 1280 626 152 220 54 1160 1093 548 393 362 1097 229 379 42 1194 647 1366