4-manifolds and kirby calculus pdf notes

However, as powerful as these invariants are, they cannot distinguish all 4manifolds. But now note that by the universal coefficient theorem. I am also indebted to the pure mathematics faculty here at the university of waterloo. The topology of 4manifolds, volume 74 of lecture notes in mathematics. A framed link in the 3sphere encodes instructions for attaching 2handles to the 4 ball. Symplectic structures on the cotangent bundles of open 4. Graduate students, nonexperts, and experts alike will enjoy browsing through it. You may use the 3rd edition of this book if you wish, but make sure the hw exerfilename. Siebenmann he invented the kirbysiebenmann invariant for classifying the piecewise linear structures on a topological manifold. Download pdf 4 manifolds and kirby calculus graduate. A list of recommended books in topology cornell university. Part i of the text presents the basics of the theory at the secondyear graduate level and offers an overview of current research.

There are kirby diagrams for 3 and 4 manifolds which consist of framed links corresponding to 1 and 2handles attached to a single 0handle. By analogy, one can draw 2dimensional pictures of 3 manifolds heegaard diagrams, and 3dimensional pictures of 4 manifolds kirby diagrams. Gompf showed that a basic cut and paste operation, a symplectic normal sum, could be performed on symplectic. Are there kirby diagrams for manifolds with boundaries. Robion cromwell kirby born february 25, 1938 is a professor of mathematics at the university of california, berkeley who specializes in lowdimensional topology.

There are also various tricks to modify surgery diagrams. Stipsicz, an introduction to 4manifolds and kirby calculus, book in preparation k r. Also note that by orienting k and using the right hand rule, one normal. An extended set of diagrams and moves are used for describing 4 manifolds. Any such diagram will give a unique closed manifold since the 3 and 4 handles that close the 012handlebody are unique. In other words, smooth 4manifolds can have in nitely many exotic copies, that is, smooth 4manifolds which are homeomorphic but not di eomorphic to the given model. Recall that an scobordism is an hcobordism with vanishing whitehead torsion. As well, to terry fuller, whose paper in 2003 lefschetz fibrations of 4 dimensional manifolds was a truly invaluable source for this project. Settheoretic tools for every mathematician, 1997 17 henryk iwaniec, topics in classical automorphic forms, 1997. Kirby kirb 1 has developed a calculus to manipulate handle decompositions of 4manifolds which can be used to prove that two. Part iii offers in depth a broad range of topics from current 4 manifold research.

American mathematical society 201 charles street providence, rhode island 0290422 4014554000 or 8003214267. Good covers by stein manifolds every complex manifold admits a good cover by stein manifolds, in the sense that all finite nonempty intersections of the cover are stein manifolds e. Morgan, the seibergwitten equations and applications to the topology of smooth fourmanifolds, math. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. Sev 1 francesco severi, intorno ai punti doppi impropri di una superficie generale dello spazio a quattro dimensioni, e a suoi punti tripli apparenti, rend. Part iii offers in depth a broad range of topics from current 4manifold research. Most of the proofs are new or are returbishings of post proofs.

Calculus 4th edition by michael spivak free pdf file sharing. 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 ii is devoted to an exposition of kirby calculus, or handle body theory on 4 manifolds. Knots, links, and 4manifolds article pdf available in inventiones mathematicae 42. Note that while the first homology h1x clearly doesnt distinguish. Lp, which says that any connected smooth 4manifold is determined by its 1 and 2handles.

Stipsicz, 4 manifolds and kirby calculus, 1999 19 lawrence c. Evans, partial differential equations, 1998 18 winfried just and martin weese, discovering modern set theory. A stein manifold is necessarily a noncompact topological space. Kirby, problems in lowdimensional topology, in geometric topology w. Questions tagged kirbydiagram mathematics stack exchange. Pdf an explicit derivation of the elements of the representation ring of su2 needed to implement the fourdimensional kirby calculus is sketched. Part ii is devoted to an exposition of kirby calculus, or handlebody theory on 4manifolds.

Selected titles in this series american mathematical society. In this paper, we investigate existence of inequivalent smooth structures on closed smooth nonorientable 4manifolds building upon results of akbulut, cappellshaneson, fintushelstern, gompf and s. A smooth 4 manifold is a 4 manifold with a smooth structure. Smooth structures on nonorientable fourmanifolds and free. Kirby, university of california, berkeley this book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Part ii is devoted to an exposition of kirby calculus, or handlebody theory on 4 manifolds. In these notes, adapted from six lectures given at the 2006 park.

With the help of open books one can likewise represent at least some 5 manifolds by 3dimensional diagrams, and contact geometry can be used to reduce these to drawings in the 2plane. Monopoles and threemanifolds, volume 10 of new mathematical monographs. Kirby calculus is a little bit more complicated than in the threedimensional case. Stipsicz, 4manifoldsandkirbycalculus,1999 19 lawrence c.

Gompf and stipsicz 4manifolds and kirby calculus 4, roughly from front to finish. Stipsicz 4 manifolds and kirby calculus, and alexandru scorpan the wild world of 4 manifolds, amongst many others. This book presents the classical theorems about simply connected smooth 4 manifolds. Jul 30, 20 let x 0 and x 1 be smooth, open, homeomorphic 4manifolds. A good source on 4manifold topology is robert gompf and andr as stipsicz 4manifolds and kirby calculus.