Hempel, 3 manifolds as viewed from the curve complex, topology 40 2001, no. This book grew out of a graduate course on 3 manifolds and is intended for a mathematically experienced audience that is new to lowdimensional topology. Preface to the second edition this is a completely revised edition, with more than. Thus the splittings provided by hempel s theorem must represent in. Manifolds scott 1977 bulletin of the london mathematical society wiley online library.
Hempel, 3 manifolds as viewed from the curve complex, topology 40 3 2001 631657 used the curve complex associated to the heegaard surface of a splitting of a 3 manifold to. Syllabus for introduction to hyperbolic 2 and 3 manifolds math 8790, spring 2014 albert marden february 4, 2014 some references. Flat drawings are twodimensional, as is appropriate for the surface of a sphere, a 2 manifold. The virtually special machine currently o ers no e ective method for determining, given an arbitrary hyperbolic 3 manifold m, the index of a subgroup of.
We remark that the second author has proved that each. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. Except for pagination, this version is identical with the published version we have had a longstanding interest in the way that structure in the mapping class group of a. Given a compact, hyperbolizable 3 manifold m, a uniformization of m is a kleinian group.
By adding one or two necks if necessary, we can merge them into a. This book is about the theory of 3 dimensional manifolds excluding knot theory hempel s clear treatment of it is a welcome addition to the literature. There are two topological processes to join 3 manifolds to get a new one. By adding one or two necks if necessary, we can merge them into a larger subset. Hempel, 3manifolds, princeton university press 1976. Threedimensional manifolds michaelmas term 1999 prerequisites basic general topology eg. In low dimensions, we have that rp0 is just a point, while rp1 is a circle.
American mathematical society 201 charles street providence, rhode island 0290422 4014554000 or 8003214267 ams, american mathematical society, the tricolored ams logo, and advancing research, creating connections, are trademarks and services marks of the american mathematical society and registered in the u. This book is about 30 years old and doesnt even mention the geometrization conjecture of thurston. The theme of this book is the role of the fundamental group in determining the topology of a given 3manifold. Introduction to 3 manifolds 5 the 3 torus is a 3 manifold constructed from a cube in r3. A 3 manifold can be thought of as a possible shape of the universe. Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. A seifert fiber space is a 3manifold together with a decomposition as a disjoint union of circles. A smooth map taking an open set in the plane onto an open set in a surface is called a smooth parametrisation of that part of the surface. In other words, it is a bundle circle bundle over a 2dimensional orbifold. Thurston the geometry and topology of threemanifolds. Syllabus for introduction to hyperbolic 2 and 3manifolds. We follow the book introduction to smooth manifolds by john m.
Homology and dimension of proximity spaces preuss, gerhard, tsukuba journal of mathematics, 1991. Most beginning graduate students have had undergraduate courses in algebra and analysis, so that graduate courses in those areas are continuations of subjects they have already be. Preface these are notes of lectures on kahler manifolds which i taught at the university of bonn and, in reduced form, at the erwinschr. Let each face be identi ed with its opposite face by a translation without twisting. Just as a sphere looks like a plane to a small enough observer, all 3 manifolds look like our universe does to a small enough observer. Below is list of references for reading on above topics. However, in general a manifold need not be given or considered as lying in some ambient euclidean space. Hempel and mcmillan showed that a closed 3manifold that can be covered by three open balls is a connected sum of s3 and s2bundles over s1. The homology of a 3 manifold can be computed from a heegaard splitting, using mayervietoris. Milnor, remarks concerning spin manifolds, differential and combinatorial topology, a symposium in honor of marston morse, princeton univ. A heegaard diagram for a 3manifold is regarded as a pair of simplexes in the. Most of the really interesting examples of manifolds will have to wait until chapter 5, however.
Later chapters address more advanced topics, including waldhausens theorem on a class of 3manifolds that is completely determined by its fundamental group. Let m be a 3manifold, and b a compact surface contained. An open set c of m is acategorical if there exist maps. For many years, john hempel s book has been a standard text,anifolds the topology of 3manifolds.
Hempel is a great place to challenge yourself and expand your horizons. As the fundamental group already determines the homology of a oriented, closed compact 3 manifold, it has to be a homology sphere. High distance heegaard splittings of 3manifolds core. This is a collection of sketches of elementary 3 manifolds. The result is a compact 2manifold with nonempty boundary. Combining the jsj decomposition theorem with the elliptization theorem. Nov 02, 2004 later chapters address more advanced topics, including waldhausens theorem on a class of 3manifolds that is completely determined by its fundamental group.
The topology of 3manifolds, heegaard distance and the. How can one prove that two knots can or cannot be deformed into each other. Pdf computing fundamental group of general 3manifold. The exhaust gas expelled from the engines combustion chamber by the piston is known as an exhaust pulse. Thus, for connected 1 manifolds, two invariants, compactness and presence of boundary, form a complete system of topological invariants. Text useful references for some of the topics we will cover include the book of kirby and. Since c does not separate f, d is a meridiandisk of hi by the isotopy of type a at a, a new projective plane p is obtained.
With the geometrization conjecture, this now holds for any compact and orientable 3manifold. Section 3 play an important role in our proof of theorem 4. This in turn implies linear geodesic residual niteness growth for every closed hyperbolic 3 manifold, see 16, lemma 6. How is a hip how is a hip part produced part produced.
You can imagine this as a direct extension from the 2torus we are comfortable with. The hempel distance is then the smallest value of k amongst all such sequences. Qhomology planes as cyclic covers of a2 maharana, alok, journal of the mathematical society of japan, 2009. The first is the connected sum of two manifolds and. Hempel, \3manifolds, annals of mathematics studies 86, princeton univ. Hempel s book remains an ideal text to learn about the world of 3manifolds. A note on hempel mcmillan coverings of 3 manifolds. Finite group actions and 3manifold topology rims, kyoto. The book concludes with a list of problems that were unsolved at the time of publication. Mapping tori, handle decompositions from the standpoint of morse theory, heegaard splittings, and dehn surgeries along knots and links.
Eventually this set will grow trying to illustrate all the most evident spaces, something like the list in, thing that is not very popular in general but growing in the public domain. Our emphasis will be on manifolds of low dimension 3 and cases where it is possible to obtain very precise information such as computing the homotopy type of di eomorphism groups. Sidharth kshatriya under my guidance during the academic year 20062007. Combinatorial problems and exercises laszlo lovasz. Simple to complex with some numerical computations, was completed by mr. A little more precisely it is a space together with a way of identifying it locally with a euclidean space which is compatible on overlaps. Then any two smooth atlases for mdetermine the same smooth structure if and only if their union is a smooth. Coverings of 3manifolds by open balls and two open solid. Then there exists a nonzero element of having a representative that is an. Thurstons threedimensional geometry and topology, vol. High distance heegaard splittings of 3manifolds request pdf.
Finite volume hyperbolic 3manifolds whose fundamental. The present book is a mixture of an introductory text book on the geometrictopological theory of 3 manifolds and a guide to some recent developments. The proof of these, and many other theorems in 3manifold topology, depend on com. Thurston, the geometry and topology of 3 manifolds. He introduced the distance of a heegaard splitting as the. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for. Finite group actions on other geometric 3manifolds are studied by meeks and. Here, and throughout these lectures, manifold will always mean a smooth, compact, connected, orientable manifold, we will not assume though that manifolds are closed. The references that will be primarily followed are indicated in red color. Most 3manifolds are seifert fiber spaces, and they account for all compact oriented manifolds in 6 of the 8 thurston geometries. In mathematics, a 3 manifold is a space that locally looks like euclidean 3 dimensional space. Introduction to differentiable manifolds lecture notes version 2. Curves and surfaces are examples of manifolds of dimension d 1 and d 2 respectively.
Important types of 3 manifolds are haken manifolds, seifert manifolds, 3 dimensional lens spaces, torusbundles and torus semibundles. Calculus on manifolds a solution manual forspivak1965 jianfei shen school of economics, the university of new south wales sydney, australia 2010. Log style one of the purposes of an exhaust manifold on a turbo charged engine is to act as a exhaust gas delivery device from the cylinder head to the turbine side of the turbo. Hempel and mcmillan showed that a closed 3 manifold that can be covered by three open balls is a connected sum of s3 and s2bundles over s1. Prime 3 manifolds can be distinguished by their fundamental groups into the following 3 types. Qiu, the amalgamation of high distance heegaard splittings is. Manifolds cm437zcmms18 neil lambert department of mathematics kings college london strand london wc2r 2ls, u. Summary of previous research on the virtual conjectures.
Click on the link to download or obtain more information on each reference. Hempel proved that haken manifolds have residually finite fundamental groups. All manifolds assumed to be connected and compact, but no assumptions on orientability or type of the boundary. Princeton university press, university of tokyo press, 1976. In mathematics, in the topology of 3 manifolds, the sphere theorem of christos papakyriakopoulos gives conditions for elements of the second homotopy group of a 3 manifold to be represented by embedded spheres one example is the following. Heegaard splittings of 3 manifolds with generic gluing maps in this section, the homology of 3 manifolds described as heegaard splittings with generic gluing maps will be studied.
Clearly the requirement that the neighborhoods be open means that in a connected space, such as the circle written as the union of two open neighborhoods, those neighborhoods must have open, nonempty intersection. We then discuss in some detail how local coordinates can be used to identify parts of smooth manifolds locally. Chapter 1 introduction a course on manifolds differs from most other introductory graduate mathematics courses in that the subject matter is often completely unfamiliar. I could cite half a dozen other books that say the same thing. Examples s3, s1 s1 s1, rp3, s3 ntubular neighborhood of a knot. Knots play an important role in the theory, not only theoretically. Thus every topological 3 manifold has a unique smooth structure, and the. With the geometrization conjecture, this now holds for any compact and orientable 3 manifold. On the structure of manifolds with positive scalar.
Let a be a point, a 1sphere s1, a 2sphere s2, a projective plane p2,a2dimensional torus t2, or a 2dimensional klein bottle k2. This tutorial will introduce the theory of knots and 3 dimensional manifolds. Tu 14 june 2 july, 2010 tufts university medford ma usa an introduction to manifolds. The universal cover is a simplyconnected 3 manifold. Combining the jsj decomposition theorem with the elliptization theorem and the. For many years, john hempels book has been a standard text on the topology of 3manifolds. David bachman, mario eudavemunoz, john hempel, tao li, yair minsky, yoav moriah and richard weidmann. Hempel, 3 manifolds as viewed from the curve complex, topology 40 3 2001 631657 used the curve complex associated to the heegaard surface of a splitting of a 3 manifold to study its complexity. In keeping with the conventional meaning of chapters and. The existence of negatively ricci curved metrics on three. A reference for any facts about heegaards splitting used here is 6. A pleasant feature of 3 manifolds, in contrast to higher dimensions, is that there thus every topological 3 manifold has a unique smooth structure, and the j hempel. Let be an orientable 3 manifold such that is not the trivial group.
The solution manual is written by guitjan ridderbos. Check our vacancies or find out more about working at hempel. Summer school and conference on hodge theory and related topics. The topology of 3 manifolds, heegaard distance and the mapping class group of a 2 manifold. For many years, john hempel s book has been a standard text on the topology of 3manifolds.
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