3 Manifold Groups
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3 Manifold Groups
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Author : Matthias Aschenbrenner
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2015
3 Manifold Groups written by Matthias Aschenbrenner and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Fundamental groups (Mathematics) categories.
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.
3 Manifold Groups Are Virtually Residually P
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Author : Matthias Aschenbrenner
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-08-23
3 Manifold Groups Are Virtually Residually P written by Matthias Aschenbrenner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Mathematics categories.
Given a prime , a group is called residually if the intersection of its -power index normal subgroups is trivial. A group is called virtually residually if it has a finite index subgroup which is residually . It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually for all but finitely many . In particular, fundamental groups of hyperbolic -manifolds are virtually residually . It is also well-known that fundamental groups of -manifolds are residually finite. In this paper the authors prove a common generalization of these results: every -manifold group is virtually residually for all but finitely many . This gives evidence for the conjecture (Thurston) that fundamental groups of -manifolds are linear groups.
3 Manifolds
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Author : John Hempel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-11-02
3 Manifolds written by John Hempel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-02 with Mathematics categories.
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.
Imbeddings Of Three Manifold Groups
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Author : Francisco González-Acuña
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Imbeddings Of Three Manifold Groups written by Francisco González-Acuña and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This work deals with the two broad questions of how three-manifold groups imbed in one another and how such imbeddings relate to any corresponding $\pi _1$-injective maps. The focus is on when a given three-manifold covers another given manifold. In particular, the authors are concerned with 1) determining which three-manifold groups are not cohopfian--that is, which three-manifold groups imbed properly in themselves; 2) finding the knot subgroups of a knot group; and 3) investigating when surgery on a knot $K$ yields lens (or ``lens-like'') spaces and how this relates to the knot subgroup structure of $\pi _1(S^3-K)$. The authors use the formulation of a deformation theorem for $\pi _1$-injective maps between certain kinds of Haken manifolds and develop some algebraic tools.
Knots Groups And 3 Manifolds Am 84 Volume 84
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Author : Lee Paul Neuwirth
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Knots Groups And 3 Manifolds Am 84 Volume 84 written by Lee Paul Neuwirth and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.
Topology And Combinatorics Of 3 Manifolds
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Author : Klaus Johannson
language : en
Publisher: Springer
Release Date : 2006-11-14
Topology And Combinatorics Of 3 Manifolds written by Klaus Johannson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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
Homotopy Equivalences Of 3 Manifolds With Boundaries
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Author : K. Johannson
language : en
Publisher: Springer
Release Date : 2006-11-15
Homotopy Equivalences Of 3 Manifolds With Boundaries written by K. Johannson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Introduction To 3 Manifolds
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Author : Jennifer Schultens
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-05-21
Introduction To 3 Manifolds written by Jennifer Schultens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-21 with Mathematics categories.
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.
Hyperbolic Manifolds And Discrete Groups
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Author : Michael Kapovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-04
Hyperbolic Manifolds And Discrete Groups written by Michael Kapovich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-04 with Mathematics categories.
Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.
Subgroup Separability Of 3 Manifold Groups
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Author : Saburo Matsumoto
language : en
Publisher:
Release Date : 1995
Subgroup Separability Of 3 Manifold Groups written by Saburo Matsumoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.