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Imbeddings Of Three Manifold Groups
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Book Synopsis Imbeddings of Three-Manifold Groups by : Francisco González-Acuña
Download or read book Imbeddings of Three-Manifold Groups written by Francisco González-Acuña and published by American Mathematical Soc.. This book was released on 1992 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the two broad questions of how 3-manifold groups imbed in one another and how such imbeddings relate to any corresponding [lowercase Greek]Pi1-injective maps. In particular, we are interested in 1) determining which 3-manifold groups are no cohopfian, that is, which 3-manifold groups imbed properly in themselves, 2) determining the knot subgroups of a knot group, and 3) determining when surgery on a knot [italic]K yields a lens (or "lens-like") space and the relationship of such a surgery to the knot-subgroup structure of [lowercase Greek]Pi1([italic]S3 - [italic]K). Our work requires the formulation of a deformation theorem for [lowercase Greek]Pi1-injective maps between certain kinds of Haken manifolds and the development of some algebraic tools.
Book Synopsis 3-manifold Groups by : Matthias Aschenbrenner
Download or read book 3-manifold Groups written by Matthias Aschenbrenner and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2015 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Embeddings in Manifolds by : Robert J. Daverman
Download or read book Embeddings in Manifolds written by Robert J. Daverman and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.
Book Synopsis A Survey of Knot Theory by : Akio Kawauchi
Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Book Synopsis Diffeomorphisms of Elliptic 3-Manifolds by : Sungbok Hong
Download or read book Diffeomorphisms of Elliptic 3-Manifolds written by Sungbok Hong and published by Springer. This book was released on 2012-08-29 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Handbook of Geometric Topology by : R.B. Sher
Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Book Synopsis Gorenstein Quotient Singularities in Dimension Three by : Stephen Shing-Toung Yau
Download or read book Gorenstein Quotient Singularities in Dimension Three written by Stephen Shing-Toung Yau and published by American Mathematical Soc.. This book was released on 1993 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In chapter one we address the classification of finite subgroups of [italic capitals]SL([bold]3,[double-struck capital]C). This is followed by a general method to find invariant polynomials and their relations of finite subgroups of [italic capitals]GL([bold]3,[double-struck capital]C). Lastly, we recall some properties of quotient varieties and prove that [double-struck capital]C3/[italic capital]G has isolated singularities if and only if [italic capital]G is abelian and 1 is not an eigenvalue of g in [italic capital]G.
Book Synopsis Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by : Jaume Llibre
Download or read book Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations written by Jaume Llibre and published by American Mathematical Soc.. This book was released on 1994 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of "almost all" the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.
Book Synopsis Coarse Cohomology and Index Theory on Complete Riemannian Manifolds by : John Roe
Download or read book Coarse Cohomology and Index Theory on Complete Riemannian Manifolds written by John Roe and published by American Mathematical Soc.. This book was released on 1993 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: "July 1993, volume 104, number 497 (fourth of 6 numbers)."
Book Synopsis Minimal Surfaces in Riemannian Manifolds by : Min Ji
Download or read book Minimal Surfaces in Riemannian Manifolds written by Min Ji and published by American Mathematical Soc.. This book was released on 1993 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multiple solution theory to the Plateau problem in a Riemannian manifold is established. In [italic capital]S[superscript italic]n, the existence of two solutions to this problem is obtained. The Morse-Tompkins-Shiffman Theorem is extended to the case when the ambient space admits no minimal sphere.
Book Synopsis Invariant Subsemigroups of Lie Groups by : Karl-Hermann Neeb
Download or read book Invariant Subsemigroups of Lie Groups written by Karl-Hermann Neeb and published by American Mathematical Soc.. This book was released on 1993 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: First we investigate the structure of Lie algebras with invariant cones and give a characterization of those Lie algebras containing pointed and generating invariant cones. Then we study the global structure of invariant Lie semigroups, and how far Lie's third theorem remains true for invariant cones and Lie semigroups.
Book Synopsis $(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ by : Maria del Rosario Gonzalez-Dorrego
Download or read book $(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ written by Maria del Rosario Gonzalez-Dorrego and published by American Mathematical Soc.. This book was released on 1994 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.
Book Synopsis Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions by : Percy Deift
Download or read book Loop Groups, Discrete Versions of Some Classical Integrable Systems, and Rank 2 Extensions written by Percy Deift and published by American Mathematical Soc.. This book was released on 1992 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors show how to interpret recent results of Moser and Veselov on discrete versions of a class of classical integrable systems, in terms of a loop group framework. In this framework the discrete systems appear as time-one maps of integrable Hamiltonian flows. Earlier results of Moser on isospectral deformations of rank 2 extensions of a fixed matrix, can also be incorporated into their scheme.
Download or read book Knots 90 written by Akio Kawauchi and published by Walter de Gruyter. This book was released on 1992 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory by : Abhijit Champanerkar
Download or read book Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory written by Abhijit Champanerkar and published by American Mathematical Soc.. This book was released on 2011 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.
Book Synopsis Unraveling the Integral Knot Concordance Group by : Neal W. Stoltzfus
Download or read book Unraveling the Integral Knot Concordance Group written by Neal W. Stoltzfus and published by American Mathematical Soc.. This book was released on 1977 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.
Book Synopsis Degenerate Principal Series for Symplectic Groups by : Chris Jantzen
Download or read book Degenerate Principal Series for Symplectic Groups written by Chris Jantzen and published by American Mathematical Soc.. This book was released on 1993 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with induced representations for $p$-adic groups. In particular, Jantzen examines the question of reducibility in the case where the inducing subgroup is a maximal parabolic subgroup of $Sp_{2n (F)$ and the inducing representation is one-dimensional. Two different approaches to this problem are used. The first, based on the work of Casselman and of Gustafson, reduces the problem to the corresponding question about an associated finite-dimensional representation of a certain Hecke algebra. The second approach is based on a technique of Tadi\'c and involves an analysis of Jacquet modules. This is used to obtain a more general result on induced representations, which may be used to deal with the problem when the inducing representation satisfies a regularity condition. The same basic argument is also applied in a case-by-case fashion to nonregular cases.
