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The Theory of Infinite Soluble Groups
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198507284.jpg" alt="The Theory of Infinite Soluble Groups"/><br/></td><td><dl><dt>Author:</dt><dd>John C. Lennox, Derek J. S. Robinson</dd><dt>ISBN:</dt><dd>9780198507284</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198507284.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev completions, soluble linear groups, P. Hall’s theory of finitely generated soluble groups, soluble groups with finite rank, soluble groups whose abelian subgroups satisfy finiteness conditions, simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, centrality in finitely generated soluble groups and the Lennox-Roseblade theorem, algorithmic problems for polycyclic and metabelian groups, cohomological topics including groups with finite (co)homological dimension and vanishing theorems, finitely presented soluble groups, constructible soluble groups, the Bieri-Strebel invariant, subnormality, and soluble groups.</p>John C. Lennox and Derek J. S. Robinson2007-09-01Spectral Theory and Differential Operators
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198812050.jpg" alt="Spectral Theory and Differential Operators"/><br/></td><td><dl><dt>Author:</dt><dd>David Edmunds, Des Evans</dd><dt>ISBN:</dt><dd>9780198812050</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/oso/9780198812050.001.0001</dd><dt>Published in print:</dt><dd>2018</dd><dt>Published Online:</dt><dd>2018-09-20</dd></dl></td></tr></table><p>This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions. After the exposition of the abstract theory in the first four chapters, Sobolev spaces are introduced and their main properties established. The remaining seven chapters are largely concerned with second-order elliptic differential operators and related boundary-value problems. Particular attention is paid to the spectrum of the Schrödinger operator. Its original form contains material of lasting importance that is relatively unaffected by advances in the theory since 1987, when the book was first published. The present edition differs from the old by virtue of the correction of minor errors and improvements of various proofs. In addition, it contains Notes at the ends of most chapters, intended to give the reader some idea of recent developments together with additional references that enable more detailed accounts to be accessed.</p>David Edmunds and Des Evans2018-09-20Theories, Sites, Toposes
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198758914.jpg" alt="Theories, Sites, ToposesRelating and studying mathematical theories through topos-theoretic 'bridges'"/><br/></td><td><dl><dt>Author:</dt><dd>Olivia Caramello</dd><dt>ISBN:</dt><dd>9780198758914</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/oso/9780198758914.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2018-03-22</dd></dl></td></tr></table><p>This book is devoted to a general study of geometric theories from a topos-theoretic perspective. After recalling the necessary topos-theoretic preliminaries, it presents the main methodology it uses to extract ‘concrete’ information on theories from properties of their classifying toposes—the ‘bridge’ technique. As a first implementation of this methodology, a duality is established between the subtoposes of the classifying topos of a geometric theory and the geometric theory extensions (also called ‘quotients’) of the theory. Many concepts of elementary topos theory which apply to the lattice of subtoposes of a given topos are then transferred via this duality into the context of geometric theories. A second very general implementation of the ‘bridge’ technique is the investigation of the class of theories of presheaf type (i.e. classified by a presheaf topos). After establishing a number of preliminary results on flat functors in relation to classifying toposes, the book carries out a systematic investigation of this class resulting in a number of general results and a characterization theorem allowing one to test whether a given theory is of presheaf type by considering its models in arbitrary Grothendieck toposes. Expansions of geometric theories and faithful interpretations of theories of presheaf type are also investigated. As geometric theories can always be written (in many ways) as quotients of presheaf type theories, the study of quotients of a given theory of presheaf type is undertaken. Lastly, the book presents a number of applications in different fields of mathematics of the theory it develops.</p>Olivia Caramello2018-03-22The Fourth Janko Group
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198527596.jpg" alt="The Fourth Janko Group"/><br/></td><td><dl><dt>Author:</dt><dd>Alexander A. Ivanov</dd><dt>ISBN:</dt><dd>9780198527596</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198527596.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book illustrates how different methods of finite group theory including representation theory, cohomology theory, combinatorial group theory, and local analysis, are combined to construct one of the last of the sporadic finite simple groups — the fourth Janko group J4. This book's approach is based on analysis of group amalgams and the geometry of the complexes of these amalgams with emphasis on the underlying theory.</p>Alexander A. Ivanov2007-09-01An Alternative Approach to Lie Groups and Geometric Structures
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198821656.jpg" alt="An Alternative Approach to Lie Groups and Geometric Structures"/><br/></td><td><dl><dt>Author:</dt><dd>Ercüment H. Ortaçgil</dd><dt>ISBN:</dt><dd>9780198821656</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/oso/9780198821656.001.0001</dd><dt>Published in print:</dt><dd>2018</dd><dt>Published Online:</dt><dd>2018-09-20</dd></dl></td></tr></table><p>This book is about the foundations of geometric symmetry, namely, Lie groups and differential geometry. Although this is a classical subject about which hundreds of books have been written, this book takes a new and innovative approach. The main idea is to replace the Maurer–Cartan form with absolute parallelism and its curvature. Unlike the classical approach, where the model is fixed beforehand by the Maurer–Cartan form, this new approach is model-free, and also revisits the foundational concepts of differential geometry, such as covariant differentiation, from a different perspective.</p>Ercüment H. Ortaçgil2018-09-20Operator Algebras and Their Modules
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198526599.jpg" alt="Operator Algebras and Their ModulesAn operator space approach"/><br/></td><td><dl><dt>Author:</dt><dd>David P. Blecher, Christian Le Merdy</dd><dt>ISBN:</dt><dd>9780198526599</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198526599.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book presents the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory, and methodologies. A major trend in modern mathematics, inspired largely by physics, is toward ‘noncommutative’ or ‘quantized’ phenomena. In functional analysis, this has appeared notably under the name of ‘operator spaces’, which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in ‘noncommutative mathematics’. The category of operator spaces includes operator algebras, selfadjoint (that is, C*-algebras) or otherwise. Also, most of the important modules over operator algebras are operator spaces. A common treatment of the subjects of C*-algebras, nonselfadjoint operator algebras, and modules over such algebras (such as Hilbert C*-modules), together under the umbrella of operator space theory, is the main topic of the book. A general theory of operator algebras and their modules naturally develops out of the operator space methodology. Indeed, operator space theory is a sensitive enough medium to reflect accurately many important noncommutative phenomena. Using recent advances in the field, the book shows how the underlying operator space structure captures, very precisely, the profound relations between the algebraic and the functional analytic structures involved. The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted. Each chapter ends with a section of notes containing additional information.</p>David P. Blecher and Christian Le Merdy2007-09-01Harmonic Morphisms Between Riemannian Manifolds
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198503620.jpg" alt="Harmonic Morphisms Between Riemannian Manifolds"/><br/></td><td><dl><dt>Author:</dt><dd>Paul Baird, John C. Wood</dd><dt>ISBN:</dt><dd>9780198503620</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198503620.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic function on the codomain is a harmonic function on the domain; it thus ‘pulls back’ germs of harmonic functions to germs of harmonic functions. Harmonic morphisms can be characterized as harmonic maps satisfying a condition dual to weak conformality called ‘horizontal weak conformality’ or ‘semiconformality’. Examples include harmonic functions, conformal mappings in the plane, holomorphic mappings with values in a Riemann surface, and certain submersions arising from Killing fields and geodesic fields. The study of harmonic morphisms involves many different branches of mathematics: the book includes discussion on aspects of the theory of foliations, polynomials induced by Clifford systems and orthogonal multiplications, twistor and mini-twistor spaces, and Hermitian structures. Relations with topology are discussed, including Seifert fibre spaces and circle actions, also relations with isoparametric functions and the Beltrami fields equation of hydrodynamics.</p>Paul Baird and John C. Wood2007-09-01