3-Manifold Groups Are Virtually Residually $p$ PDF Download
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Author: Matthias Aschenbrenner
Publisher: American Mathematical Soc.
ISBN: 0821888013
Category : Mathematics
Languages : en
Pages : 114
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Book Description
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.
Author: Matthias Aschenbrenner
Publisher: American Mathematical Soc.
ISBN: 0821888013
Category : Mathematics
Languages : en
Pages : 114
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Book Description
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.
Author: Michael Usher
Publisher: American Mathematical Soc.
ISBN: 0821852353
Category : Mathematics
Languages : en
Pages : 242
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Book Description
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.
Author: Michael S. Weiss
Publisher: American Mathematical Soc.
ISBN: 147040981X
Category : Mathematics
Languages : en
Pages : 122
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Book Description
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.
Author: Florin Diacu
Publisher: American Mathematical Soc.
ISBN: 0821891367
Category : Mathematics
Languages : en
Pages : 92
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Book Description
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 ?
Author: Christopher P. Bendel
Publisher: American Mathematical Soc.
ISBN: 0821891758
Category : Mathematics
Languages : en
Pages : 110
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Book Description
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.
Author: Milen Yakimov
Publisher: American Mathematical Soc.
ISBN: 082189174X
Category : Mathematics
Languages : en
Pages : 104
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Book Description
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 .
Author: Vin de Silva
Publisher: American Mathematical Soc.
ISBN: 0821898868
Category : Mathematics
Languages : en
Pages : 126
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Book Description
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.
Author: Sy-David Friedman
Publisher: American Mathematical Soc.
ISBN: 0821894757
Category : Mathematics
Languages : en
Pages : 92
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Book Description
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.
Author: Jakob Wachsmuth
Publisher: American Mathematical Soc.
ISBN: 0821894897
Category : Mathematics
Languages : en
Pages : 96
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Book Description
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.
Author: Mark Green
Publisher: American Mathematical Soc.
ISBN: 0821898574
Category : Mathematics
Languages : en
Pages : 158
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Book Description
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.
