Invariants

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An Introduction to Quantum and Vassiliev Knot Invariants

Author : David M. Jackson
Publisher : Springer
ISBN 13 : 3030052133
Total Pages : 422 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Introduction to Quantum and Vassiliev Knot Invariants by : David M. Jackson

Download or read book An Introduction to Quantum and Vassiliev Knot Invariants written by David M. Jackson and published by Springer. This book was released on 2019-05-04 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.

Equivalence, Invariants and Symmetry

Author : Peter J. Olver
Publisher : Cambridge University Press
ISBN 13 : 9780521478113
Total Pages : 546 pages
Book Rating : 4.4/5 (781 download)

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Book Synopsis Equivalence, Invariants and Symmetry by : Peter J. Olver

Download or read book Equivalence, Invariants and Symmetry written by Peter J. Olver and published by Cambridge University Press. This book was released on 1995-06-30 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

An Introduction to Invariants and Moduli

Author : Shigeru Mukai
Publisher : Cambridge University Press
ISBN 13 : 9780521809061
Total Pages : 528 pages
Book Rating : 4.8/5 (9 download)

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Book Synopsis An Introduction to Invariants and Moduli by : Shigeru Mukai

Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9789812811172
Total Pages : 516 pages
Book Rating : 4.8/5 (111 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

Moments and Moment Invariants in Pattern Recognition

Author : Jan Flusser
Publisher : John Wiley & Sons
ISBN 13 : 9780470684764
Total Pages : 312 pages
Book Rating : 4.6/5 (847 download)

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Book Synopsis Moments and Moment Invariants in Pattern Recognition by : Jan Flusser

Download or read book Moments and Moment Invariants in Pattern Recognition written by Jan Flusser and published by John Wiley & Sons. This book was released on 2009-11-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moments as projections of an image’s intensity onto a proper polynomial basis can be applied to many different aspects of image processing. These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking. This book presents a survey of both recent and traditional image analysis and pattern recognition methods, based on image moments, and offers new concepts of invariants to linear filtering and implicit invariants. In addition to the theory, attention is paid to efficient algorithms for moment computation in a discrete domain, and to computational aspects of orthogonal moments. The authors also illustrate the theory through practical examples, demonstrating moment invariants in real applications across computer vision, remote sensing and medical imaging. Key features: Presents a systematic review of the basic definitions and properties of moments covering geometric moments and complex moments. Considers invariants to traditional transforms – translation, rotation, scaling, and affine transform - from a new point of view, which offers new possibilities of designing optimal sets of invariants. Reviews and extends a recent field of invariants with respect to convolution/blurring. Introduces implicit moment invariants as a tool for recognizing elastically deformed objects. Compares various classes of orthogonal moments (Legendre, Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates their application to image reconstruction from moments. Offers comprehensive advice on the construction of various invariants illustrated with practical examples. Includes an accompanying website providing efficient numerical algorithms for moment computation and for constructing invariants of various kinds, with about 250 slides suitable for a graduate university course. Moments and Moment Invariants in Pattern Recognition is ideal for researchers and engineers involved in pattern recognition in medical imaging, remote sensing, robotics and computer vision. Post graduate students in image processing and pattern recognition will also find the book of interest.

Invariants of Quadratic Differential Forms

Author : Oswald Veblen
Publisher :
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Invariants of Quadratic Differential Forms by : Oswald Veblen

Download or read book Invariants of Quadratic Differential Forms written by Oswald Veblen and published by . This book was released on 1927 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: An early tract for students of differential geometry and mathematical physics.

Invariants of Homology 3-Spheres

Author : Nikolai Saveliev
Publisher : Springer Science & Business Media
ISBN 13 : 9783540437963
Total Pages : 254 pages
Book Rating : 4.4/5 (379 download)

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Book Synopsis Invariants of Homology 3-Spheres by : Nikolai Saveliev

Download or read book Invariants of Homology 3-Spheres written by Nikolai Saveliev and published by Springer Science & Business Media. This book was released on 2002-09-05 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.

Polynomial Invariants of Finite Groups

Author : Larry Smith
Publisher : CRC Press
ISBN 13 : 1439864470
Total Pages : 376 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Polynomial Invariants of Finite Groups by : Larry Smith

Download or read book Polynomial Invariants of Finite Groups written by Larry Smith and published by CRC Press. This book was released on 1995-04-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by an algebraic topologist motivated by his own desire to learn, this well-written book represents the compilation of the most essential and interesting results and methods in the theory of polynomial invariants of finite groups. From the table of contents: - Invariants and Relative Invariants - Finite Generation of Invariants - Constructio

Introduction to the Algebraic Theory of Invariants of Differential Equations

Author : Konstantin Sergeevich Sibirskiĭ
Publisher : Manchester University Press
ISBN 13 : 9780719026690
Total Pages : 210 pages
Book Rating : 4.0/5 (266 download)

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Book Synopsis Introduction to the Algebraic Theory of Invariants of Differential Equations by : Konstantin Sergeevich Sibirskiĭ

Download or read book Introduction to the Algebraic Theory of Invariants of Differential Equations written by Konstantin Sergeevich Sibirskiĭ and published by Manchester University Press. This book was released on 1988 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers polynominal invariants & comitants of autonomous systems of differential equations with right-hand sides relative to various transformation groups of phase space. Contains an in-depth discussion of the two-dimensional system with quadratic right-hand sides. Features numerous applications to the qualitative theory of differential equations.

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9810246757
Total Pages : 508 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.

Invariants of Quadratic Differential Forms

Author : Joseph Edmund Wright
Publisher : Courier Corporation
ISBN 13 : 0486497682
Total Pages : 98 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Invariants of Quadratic Differential Forms by : Joseph Edmund Wright

Download or read book Invariants of Quadratic Differential Forms written by Joseph Edmund Wright and published by Courier Corporation. This book was released on 2013-06-19 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This classic monograph by a mathematician affiliated with Trinity College, Cambridge, offers a brief account of the invariant theory connected with a single quadratic differential form. A historical overview is followed by considerations of the methods of Christoffel and Lie as well as Maschke's symbolic method and explorations of geometrical and dynamical methods. 1960 edition"--

Invariants of Quadratic Differential Forms

Author :
Publisher : CUP Archive
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4./5 ( download)

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Book Synopsis Invariants of Quadratic Differential Forms by :

Download or read book Invariants of Quadratic Differential Forms written by and published by CUP Archive. This book was released on with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Basic Global Relative Invariants for Nonlinear Differential Equations

Author : Roger Chalkley
Publisher : American Mathematical Soc.
ISBN 13 : 0821839918
Total Pages : 386 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Basic Global Relative Invariants for Nonlinear Differential Equations by : Roger Chalkley

Download or read book Basic Global Relative Invariants for Nonlinear Differential Equations written by Roger Chalkley and published by American Mathematical Soc.. This book was released on 2007 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerre's success for the special case $m = 3$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any $m \geq3$, each of the $m - 2$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations. With respect to any fixed integer $\, m \geq 1$, the author begins by explicitly specifying the basic relative invariants for the class $\, \mathcal{C {m,2 $ that contains equations like $Q {m = 0$ in which $Q {m $ is a quadratic form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){2 $ is $1$.Then, in terms of any fixed positive integers $m$ and $n$, the author explicitly specifies the basic relative invariants for the class $\, \mathcal{C {m, n $ that contains equations like $H {m, n = 0$ in which $H {m, n $ is an $n$th-degree form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){n $ is $1$.These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equa

L2-Invariants: Theory and Applications to Geometry and K-Theory

Author : Wolfgang Lück
Publisher : Springer Science & Business Media
ISBN 13 : 3662046873
Total Pages : 604 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück

Download or read book L2-Invariants: Theory and Applications to Geometry and K-Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Invariants of the Finite Continuous Groups of the Plane ...

Author : David Andrew Rothrock
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Invariants of the Finite Continuous Groups of the Plane ... by : David Andrew Rothrock

Download or read book Invariants of the Finite Continuous Groups of the Plane ... written by David Andrew Rothrock and published by . This book was released on 1899 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cohomological Invariants in Galois Cohomology

Author : Skip Garibaldi
Publisher : American Mathematical Soc.
ISBN 13 : 0821832875
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Cohomological Invariants in Galois Cohomology by : Skip Garibaldi

Download or read book Cohomological Invariants in Galois Cohomology written by Skip Garibaldi and published by American Mathematical Soc.. This book was released on 2003 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field. The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here. The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number th

Cohomological Invariants: Exceptional Groups and Spin Groups

Author : Skip Garibaldi
Publisher : American Mathematical Soc.
ISBN 13 : 0821844040
Total Pages : 102 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Cohomological Invariants: Exceptional Groups and Spin Groups by : Skip Garibaldi

Download or read book Cohomological Invariants: Exceptional Groups and Spin Groups written by Skip Garibaldi and published by American Mathematical Soc.. This book was released on 2009-06-05 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.