Geometry Of Semilinear Embeddings

Author : Mark Pankov
Publisher : World Scientific
ISBN 13 : 9814651095
Total Pages : 180 pages
Book Rating : 4.97/5 ( download)

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Download or read book Geometry of Semilinear Embeddings written by Mark Pankov and published by World Scientific. This book was released on 2015-05-28 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples. Contents:Semilinear Mappings:Division Rings and Their HomomorphismsVector Spaces Over Division RingsSemilinear MappingsSemilinear EmbeddingsMappings of Grassmannians Induced by Semilinear EmbeddingsKreuzer's ExampleDualityCharacterization of Strong Semilinear EmbeddingsProjective Geometry and Linear Codes:Projective SpacesFundamental Theorem of Projective GeometryProof of Theorem 1.2m-independent Subsets in Projective SpacesPGL-subsetsGeneralized MacWilliams TheoremLinear CodesIsometric Embeddings of Grassmann Graphs:Graph TheoryElementary Properties of Grassmann GraphsEmbeddingsIsometric EmbeddingsProof of Theorem 3.1Equivalence of Isometric EmbeddingsLinearly Rigid Isometric EmbeddingsRemarks on Non-isometric EmbeddingsSome Results Related to Chow's TheoremHuang's TheoremJohnson Graph in Grassmann Graph:Johnson GraphIsometric Embeddings of Johnson Graphs in Grassmann GraphsProof of Theorem 4.2Classification Problem and Relations to Linear CodesCharacterizations of Apartments in Building GrassmanniansCharacterization of Isometric Embeddings:Main Result, Corollaries and RemarksCharacterization of DistanceConnectedness of the Apartment GraphIntersections of J(n, k)-subsets of Different TypesProof of Theorem 5.1Semilinear Mappings of Exterior Powers:Exterior PowersGrassmanniansGrassmann Codes Readership: Graduate students and researchers interested in the field of semilinear embeddings. Keywords:Semilinear Embedding;Grassmannian;Grassmann Graph;Linear Code

Author : Robert J. Daverman
Publisher : American Mathematical Soc.
ISBN 13 : 0821836978
Total Pages : 496 pages
Book Rating : 4.72/5 ( download)

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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.

Author : Felix Schlenk
Publisher : Walter de Gruyter
ISBN 13 : 3110178761
Total Pages : 260 pages
Book Rating : 4.60/5 ( download)

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Download or read book Embedding Problems in Symplectic Geometry written by Felix Schlenk and published by Walter de Gruyter. This book was released on 2005 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Author : G. Kempf
Publisher : Springer
ISBN 13 : 3540377557
Total Pages : 210 pages
Book Rating : 4.59/5 ( download)

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Download or read book Toroidal Embeddings 1 written by G. Kempf and published by Springer. This book was released on 2006-11-15 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Claude-Alain Faure
Publisher : Springer Science & Business Media
ISBN 13 : 9401595909
Total Pages : 370 pages
Book Rating : 4.02/5 ( download)

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Download or read book Modern Projective Geometry written by Claude-Alain Faure and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.

Author : Mark Pankov
Publisher : Cambridge University Press
ISBN 13 : 1108790917
Total Pages : 154 pages
Book Rating : 4.18/5 ( download)

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Download or read book Wigner-Type Theorems for Hilbert Grassmannians written by Mark Pankov and published by Cambridge University Press. This book was released on 2020-01-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the geometric approach to Wigner's theorem and its role in quantum mechanics.

Author : Mahir Can
Publisher : Springer
ISBN 13 : 149390938X
Total Pages : 360 pages
Book Rating : 4.84/5 ( download)

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Download or read book Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics written by Mahir Can and published by Springer. This book was released on 2014-06-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.

Author : William M. Kantor
Publisher : Cambridge University Press
ISBN 13 : 052146790X
Total Pages : 324 pages
Book Rating : 4.02/5 ( download)

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Download or read book Groups of Lie Type and Their Geometries written by William M. Kantor and published by Cambridge University Press. This book was released on 1995-01-12 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Silk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.

Author : Marino Badiale
Publisher : Springer Science & Business Media
ISBN 13 : 0857292277
Total Pages : 204 pages
Book Rating : 4.78/5 ( download)

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Download or read book Semilinear Elliptic Equations for Beginners written by Marino Badiale and published by Springer Science & Business Media. This book was released on 2010-12-07 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.

Author : D.A. Timashev
Publisher : Springer
ISBN 13 : 9783642184000
Total Pages : 254 pages
Book Rating : 4.06/5 ( download)

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Download or read book Homogeneous Spaces and Equivariant Embeddings written by D.A. Timashev and published by Springer. This book was released on 2011-04-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of "combinatorial" nature (the Luna-Vust theory) and description of various geometric and representation-theoretic properties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress obtained in and around the theory of spherical varieties.