Seifert Fibered Spaces in 3-Manifolds PDF Download
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Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821822209
Category : Fiber spaces
Languages : en
Pages : 204
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Book Description
The main theorem of this monograph, or rather the "absolute" case of the main theorem, provides what is essentially a homotopy-classification of suitably "nondegenerate" maps of Seifert-fibered 3-manifolds into a sufficiently-large, compact, irreducible, orientable 3-manifold M.
Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821822209
Category : Fiber spaces
Languages : en
Pages : 204
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Book Description
The main theorem of this monograph, or rather the "absolute" case of the main theorem, provides what is essentially a homotopy-classification of suitably "nondegenerate" maps of Seifert-fibered 3-manifolds into a sufficiently-large, compact, irreducible, orientable 3-manifold M.
Author: Sungbok Hong
Publisher: Springer
ISBN: 364231564X
Category : Mathematics
Languages : en
Pages : 163
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Book Description
This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background
Author: Danny Calegari
Publisher: Oxford University Press on Demand
ISBN: 0198570082
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author: Ahmad Issa Khalid Issa
Publisher:
ISBN:
Category :
Languages : en
Pages : 290
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Book Description
This dissertation is concerned with the question of which Seifert fibered spaces smoothly embed in the 4-sphere and the related question of which Seifert fibered spaces bound both a positive definite and a negative definite smooth 4-manifold. Using Donaldson’s diagonalization theorem we derive strong obstructions in both of these settings. We construct new embeddings of Seifert fibered spaces in S4 out of old ones, giving many new examples of Seifert fibered spaces which embed in S4 . Our results allow us to classify precisely when a Seifert fibered space over an orientable base surface smoothly embeds in S4 provided e > k/2, where e is the normalized central weight and k is the number of singular fibers. Based on these results and an analysis of the Neumann-Siebenmann invariant [mu with macron], we make some conjectures concerning Seifert fibered spaces which embed in S4. Finally, we classify the quasi-alternating Montesinos links, showing that a Montesinos link L is quasialternating if and only if its double branched cover is an L-space which bounds definite manifolds of both signs with torsion-free first homology
Author: Jennifer Schultens
Publisher: American Mathematical Soc.
ISBN: 1470410206
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. 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 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Author: Matthias Aschenbrenner
Publisher: Erich Schmidt Verlag GmbH & Co. KG
ISBN: 9783037191545
Category : Fundamental groups (Mathematics)
Languages : en
Pages : 236
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Book Description
The field of 3-manifold topology has made great strides forward since 1982 when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari-Gabai, the Surface Subgroup Theorem of Kahn-Markovic, the work of Wise and others on special cube complexes, and, finally, Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focusing on the consequences for fundamental groups of 3-manifolds. As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material. Although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students. The book closes with an extensive list of open questions which will also be of interest to graduate students and established researchers.
Author: Peter Orlik
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 174
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Book Description
Author: I.M. James
Publisher: Elsevier
ISBN: 0080534074
Category : Mathematics
Languages : en
Pages : 1067
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Book Description
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Author: Klaus Johannson
Publisher: Springer
ISBN: 3540491813
Category : Mathematics
Languages : en
Pages : 464
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Book Description
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds
Author: John Hempel
Publisher: American Mathematical Society
ISBN: 1470471647
Category : Mathematics
Languages : en
Pages : 209
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Book Description
A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. —Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication. Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.
