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Quasi Actions On Trees Ii Finite Depth Bass Serre Trees
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Book Synopsis Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees by : Lee Mosher
Download or read book Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees written by Lee Mosher and published by American Mathematical Soc.. This book was released on 2011 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if $\mathcal{G}$ is a finite graph of coarse Poincare duality groups, then any finitely generated group quasi-isometric to the fundamental group of $\mathcal{G}$ is also the fundamental group of a finite graph of coarse Poincare duality groups, and any quasi-isometry between two such groups must coarsely preserve the vertex and edge spaces of their Bass-Serre trees of spaces. Besides some simple normalization hypotheses, the main hypothesis is the ``crossing graph condition'', which is imposed on each vertex group $\mathcal{G}_v$ which is an $n$-dimensional coarse Poincare duality group for which every incident edge group has positive codimension: the crossing graph of $\mathcal{G}_v$ is a graph $\epsilon_v$ that describes the pattern in which the codimension 1 edge groups incident to $\mathcal{G}_v$ are crossed by other edge groups incident to $\mathcal{G}_v$, and the crossing graph condition requires that $\epsilon_v$ be connected or empty.
Book Synopsis Quasi-actions on Trees II by : Lee Mosher
Download or read book Quasi-actions on Trees II written by Lee Mosher and published by . This book was released on 2011 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Directions in Locally Compact Groups by : Pierre-Emmanuel Caprace
Download or read book New Directions in Locally Compact Groups written by Pierre-Emmanuel Caprace and published by Cambridge University Press. This book was released on 2018-02-08 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.
Book Synopsis Weighted Shifts on Directed Trees by : Zenon Jan Jablónski
Download or read book Weighted Shifts on Directed Trees written by Zenon Jan Jablónski and published by American Mathematical Soc.. This book was released on 2012 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and of weighted adjacency operators, on the other; they are called weighted shifts on directed trees. The basic properties of such operators, including closedness, adjoints, polar decomposition and moduli are studied. Circularity and the Fredholmness of weighted shifts on directed trees are discussed. The relationships between domains of a weighted shift on a directed tree and its adjoint are described. Hyponormality, cohyponormality, subnormality and complete hyperexpansivity of such operators are entirely characterized in terms of their weights. Related questions that arose during the study of the topic are solved as well.
Book Synopsis An Invitation to Coarse Groups by : Arielle Leitner
Download or read book An Invitation to Coarse Groups written by Arielle Leitner and published by Springer Nature. This book was released on 2024-01-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms “up to uniformly bounded error”. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels. The first aim is to provide a standard entry-level introduction to coarse groups. Extra care has been taken to give a detailed, self-contained and accessible account of the theory. The second aim is to quickly bring the reader to the forefront of research. This is easily accomplished, as the subject is still young, and even basic questions remain unanswered. Reflecting its dual purpose, the book is divided into two parts. The first part covers the fundamentals of coarse groups and their actions. Here the theory of coarse homomorphisms, quotients and subgroups is developed, with proofs of coarse versions of the isomorphism theorems, and it is shown how coarse actions are related to fundamental aspects of geometric group theory. The second part, which is less self-contained, is an invitation to further research, where each thread leads to open questions of varying depth and difficulty. Among other topics, it explores coarse group structures on set-groups, groups of coarse automorphisms and spaces of controlled maps. The main focus is on connections between the theory of coarse groups and classical subjects, including: number theory; the study of bi-invariant metrics on groups; quasimorphisms and stable commutator length; groups of outer automorphisms; and topological groups and their actions. The book will primarily be of interest to researchers and graduate students in geometric group theory, topology, category theory and functional analysis, but some parts will also be accessible to advanced undergraduates.
Book Synopsis Geometric Group Theory by : Cornelia Druţu
Download or read book Geometric Group Theory written by Cornelia Druţu and published by American Mathematical Soc.. This book was released on 2018-03-28 with total page 841 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.
Book Synopsis The Hermitian Two Matrix Model with an Even Quartic Potential by : Maurice Duits
Download or read book The Hermitian Two Matrix Model with an Even Quartic Potential written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.
Book Synopsis Hopf Algebras and Congruence Subgroups by : Yorck Sommerhäuser
Download or read book Hopf Algebras and Congruence Subgroups written by Yorck Sommerhäuser and published by American Mathematical Soc.. This book was released on 2012 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, we show that the projective kernel is a congruence subgroup. To do this, we introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.
Book Synopsis Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations by : Igor Burban
Download or read book Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations written by Igor Burban and published by American Mathematical Soc.. This book was released on 2012 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: "November 2012, volume 220, number 1035 (third of 4 numbers)."
Book Synopsis Elliptic Integrable Systems by : Idrisse Khemar
Download or read book Elliptic Integrable Systems written by Idrisse Khemar and published by American Mathematical Soc.. This book was released on 2012 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.
Book Synopsis Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$ by : Aleksandr Sergeevich Kleshchëv
Download or read book Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$ written by Aleksandr Sergeevich Kleshchëv and published by American Mathematical Soc.. This book was released on 2012 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.
Book Synopsis A Theory of Generalized Donaldson-Thomas Invariants by : Dominic D. Joyce
Download or read book A Theory of Generalized Donaldson-Thomas Invariants written by Dominic D. Joyce and published by American Mathematical Soc.. This book was released on 2011 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.
Book Synopsis The Lin-Ni's Problem for Mean Convex Domains by : Olivier Druet
Download or read book The Lin-Ni's Problem for Mean Convex Domains written by Olivier Druet and published by American Mathematical Soc.. This book was released on 2012 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.
Book Synopsis On First and Second Order Planar Elliptic Equations with Degeneracies by : Abdelhamid Meziani
Download or read book On First and Second Order Planar Elliptic Equations with Degeneracies written by Abdelhamid Meziani and published by American Mathematical Soc.. This book was released on 2012 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
