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3 Manifold Groups Are Virtually Residually P
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Book Synopsis 3-Manifold Groups Are Virtually Residually $p$ by : Matthias Aschenbrenner
Download or read book 3-Manifold Groups Are Virtually Residually $p$ written by Matthias Aschenbrenner and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Low-dimensional and Symplectic Topology by : Michael Usher
Download or read book Low-dimensional and Symplectic Topology written by Michael Usher and published by American Mathematical Soc.. This book was released on 2011 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every eight years since 1961, the University of Georgia has hosted a major international topology conference aimed at disseminating important recent results and bringing together researchers at different stages of their careers. This volume contains the proceedings of the 2009 conference, which includes survey and research articles concerning such areas as knot theory, contact and symplectic topology, 3-manifold theory, geometric group theory, and equivariant topology. Among other highlights of the volume, a survey article by Stefan Friedl and Stefano Vidussi provides an accessible treatment of their important proof of Taubes' conjecture on symplectic structures on the product of a 3-manifold and a circle, and an intriguing short article by Dennis Sullivan opens the door to the use of modern algebraic-topological techniques in the study of finite-dimensional models of famously difficult problems in fluid dynamics. Continuing what has become a tradition, this volume contains a report on a problem session held at the conference, discussing a variety of open problems in geometric topology.
Book Synopsis Automorphisms of Manifolds and Algebraic $K$-Theory: Part III by : Michael S. Weiss
Download or read book Automorphisms of Manifolds and Algebraic $K$-Theory: Part III written by Michael S. Weiss and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.
Book Synopsis Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem by : Florin Diacu
Download or read book Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem written by Florin Diacu and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers the 3 -dimensional gravitational n -body problem, n32 , in spaces of constant Gaussian curvature k10 , i.e. on spheres S 3 ?1 , for ?>0 , and on hyperbolic manifolds H 3 ?1, for ?
Book Synopsis Cohomology for Quantum Groups via the Geometry of the Nullcone by : Christopher P. Bendel
Download or read book Cohomology for Quantum Groups via the Geometry of the Nullcone written by Christopher P. Bendel and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.
Book Synopsis On the Spectra of Quantum Groups by : Milen Yakimov
Download or read book On the Spectra of Quantum Groups written by Milen Yakimov and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras on simple algebraic groups in terms of the centers of certain localizations of quotients of by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of than the previously known ones and an explicit parametrization of .
Book Synopsis Combinatorial Floer Homology by : Vin de Silva
Download or read book Combinatorial Floer Homology written by Vin de Silva and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
Book Synopsis Generalized Descriptive Set Theory and Classification Theory by : Sy-David Friedman
Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy-David Friedman and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.
Book Synopsis Effective Hamiltonians for Constrained Quantum Systems by : Jakob Wachsmuth
Download or read book Effective Hamiltonians for Constrained Quantum Systems written by Jakob Wachsmuth and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.
Book Synopsis Special Values of Automorphic Cohomology Classes by : Mark Green
Download or read book Special Values of Automorphic Cohomology Classes written by Mark Green and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.
Book Synopsis Index Theory for Locally Compact Noncommutative Geometries by : A. L. Carey
Download or read book Index Theory for Locally Compact Noncommutative Geometries written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Book Synopsis To an Effective Local Langlands Correspondence by : Colin J. Bushnell
Download or read book To an Effective Local Langlands Correspondence written by Colin J. Bushnell and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F be a non-Archimedean local field. Let \mathcal{W}_{F} be the Weil group of F and \mathcal{P}_{F} the wild inertia subgroup of \mathcal{W}_{F}. Let \widehat {\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \mathcal{W}_{F}. Let \mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \mathrm{GL}_{n}(F) and set \widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F). If \sigma \in \widehat {\mathcal{W}}_{F}, let ^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F} be the cuspidal representation matched with \sigma by the Langlands Correspondence. If \sigma is totally wildly ramified, in that its restriction to \mathcal{P}_{F} is irreducible, the authors treat ^{L}{\sigma} as known. From that starting point, the authors construct an explicit bijection \mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}, sending \sigma to ^{N}{\sigma}. The authors compare this "naïve correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation \pi (of \mathcal{W}_{F} or \mathrm{GL}_{n}(F)) by tame characters of a tamely ramified field extension of F, canonically associated to \pi. The authors show this operation is preserved by the Langlands correspondence.
Book Synopsis Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem by : A. L. Carey
Download or read book Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.
Book Synopsis Weighted Bergman Spaces Induced by Rapidly Increasing Weights by : Jose Angel Pelaez
Download or read book Weighted Bergman Spaces Induced by Rapidly Increasing Weights written by Jose Angel Pelaez and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.
Book Synopsis Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids by : Hajime Koba
Download or read book Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids written by Hajime Koba and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.
Book Synopsis Stochastic Flows in the Brownian Web and Net by : Emmanuel Schertzer
Download or read book Stochastic Flows in the Brownian Web and Net written by Emmanuel Schertzer and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.
