Complexities Of 3 Manifolds From Triangulations Heegard Splittings And Surgery Presentations PDF Download
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Author | : |
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Total Pages | : |
Release | : 2017 |
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Download Complexities of 3-manifolds from Triangulations, Heegard Splittings, and Surgery Presentations Book in PDF, ePub and Kindle
Author | : Jennifer Schultens |
Publisher | : American Mathematical Soc. |
Total Pages | : 298 |
Release | : 2014-05-21 |
Genre | : Mathematics |
ISBN | : 1470410206 |
Download Introduction to 3-Manifolds Book in PDF, ePub and Kindle
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 | : Mauro Carfora |
Publisher | : Springer Science & Business Media |
Total Pages | : 298 |
Release | : 2012-01-14 |
Genre | : Science |
ISBN | : 3642244394 |
Download Quantum Triangulations Book in PDF, ePub and Kindle
Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Author | : Riccardo Benedetti |
Publisher | : Springer |
Total Pages | : 140 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540683453 |
Download Branched Standard Spines of 3-manifolds Book in PDF, ePub and Kindle
This book provides a unified combinatorial realization of the categroies of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs, and only finitely many local moves have to be taken into account. These realizations are based on the notion of branched standard spine, introduced in the book as a combination of the notion of branched surface with that of standard spine. The book is intended for readers interested in low-dimensional topology, and some familiarity with the basics is assumed. A list of questions, some of which concerning relations with the theory of quantum invariants, is enclosed.
Author | : Matthias Aschenbrenner |
Publisher | : Erich Schmidt Verlag GmbH & Co. KG |
Total Pages | : 236 |
Release | : 2015 |
Genre | : Fundamental groups (Mathematics) |
ISBN | : 9783037191545 |
Download 3-manifold Groups Book in PDF, ePub and Kindle
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 | : Saul David Schleimer |
Publisher | : |
Total Pages | : 188 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download Almost Normal Heegaard Splittings Book in PDF, ePub and Kindle
Author | : Charles Terence Clegg Wall |
Publisher | : American Mathematical Soc. |
Total Pages | : 321 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809423 |
Download Surgery on Compact Manifolds Book in PDF, ePub and Kindle
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
Author | : American Mathematical Society |
Publisher | : |
Total Pages | : 272 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : |
Download Abstracts of Papers Presented to the American Mathematical Society Book in PDF, ePub and Kindle
Author | : Danny Calegari |
Publisher | : Oxford University Press on Demand |
Total Pages | : 378 |
Release | : 2007-05-17 |
Genre | : Mathematics |
ISBN | : 0198570082 |
Download Foliations and the Geometry of 3-Manifolds Book in PDF, ePub and Kindle
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 | : |
Publisher | : |
Total Pages | : 776 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : |
Download Mathematical Reviews Book in PDF, ePub and Kindle