Inverse Invariant Theory And Steenrod Operations
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Inverse Invariant Theory And Steenrod Operations
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Inverse Invariant Theory And Steenrod Operations written by Mara D. Neusel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.
Inverse Invariant Theory And Steenrod Operations
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Author : Mara D. Neusel
language : en
Publisher:
Release Date : 2014-09-11
Inverse Invariant Theory And Steenrod Operations written by Mara D. Neusel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Invariants categories.
Introduction The $\Delta$-theorem Some field theory over the Steenrod Algebra The integral closure theorem and the unstable part The inseparable closure The embedding theorem I Noetherianess, the embedding theorem II and Turkish delights The Galois embedding theorem, the little imbedding theorem and a bit more The big imbedding theorem, Thom classes, Turkish delights II and reverse Landweber-Stong conjecture Technical stuff References.
Invariant Theory Of Finite Groups
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-03-08
Invariant Theory Of Finite Groups written by Mara D. Neusel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-08 with Mathematics categories.
The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.
Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations
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Author : Dagmar M. Meyer
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-18
Poincar Duality Algebras Macaulay S Dual Systems And Steenrod Operations written by Dagmar M. Meyer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-18 with Mathematics categories.
A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Computational Invariant Theory
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Author : Harm Derksen
language : en
Publisher: Springer
Release Date : 2015-12-23
Computational Invariant Theory written by Harm Derksen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-23 with Mathematics categories.
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
Stable Homotopy Over The Steenrod Algebra
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Author : John Harold Palmieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Stable Homotopy Over The Steenrod Algebra written by John Harold Palmieri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This title applys the tools of stable homotopy theory to the study of modules over the mod $p$ Steenrod algebra $A DEGREES{*}$. More precisely, let $A$ be the dual of $A DEGREES{*}$; then we study the category $\mathsf{stable}(A)$ of unbounded cochain complexes of injective comodules over $A$, in which the morphisms are cochain homotopy classes of maps. This category is triangulated. Indeed, it is a stable homotopy category, so we can use Brown representability, Bousfield localization, Brown-Comenetz duality, and other homotopy-theoretic tools to study it. One focus of attention is the analogue of the stable homotopy groups of spheres, which in this setting is the cohomology of $A$, $\mathrm{Ext}_A DEGREES{**}(\mathbf{F}_p, \mathbf{F}_p)$. This title also has nilpotence theorems, periodicity theorems, a convergent chromatic tower, and a nu
Invariant Measures For Unitary Groups Associated To Kac Moody Lie Algebras
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Author : Doug Pickrell
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Invariant Measures For Unitary Groups Associated To Kac Moody Lie Algebras written by Doug Pickrell and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other "invariant measures" are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.
Gorenstein Liaison Complete Intersection Liaison Invariants And Unobstructedness
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Author : Jan Oddvar Kleppe
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Gorenstein Liaison Complete Intersection Liaison Invariants And Unobstructedness written by Jan Oddvar Kleppe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. The first part establishes several basic results on Gorenstein liaison. A classical result of Gaeta on liaison classes of projectively normal curves in $\mathbb{P}^3$ is generalized to the statement that every codimension $c$ ``standard determinantal scheme'' (i.e. a scheme defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix), is in the Gorenstein liaison class of a complete intersection. Then Gorenstein liaison (G-liaison) theory is developed as a theory of generalized divisors on arithmetically Cohen-Macaulay schemes. In particular, a rather general construction of basic double G-linkage is introduced, which preserves the even G-liaison class. This construction extends the notion of basic double linkage, which plays a fundamental role in the codimension two situation. The second part of the paper studies groups which are invariant under complete intersection linkage, and gives a number of geometric applications of these invariants. Several differences between Gorenstein and complete intersection liaison are highlighted. For example, it turns out that linearly equivalent divisors on a smooth arithmetically Cohen-Macaulay subscheme belong, in general, to different complete intersection liaison classes, but they are always contained in the same even Gorenstein liaison class. The third part develops the interplay between liaison theory and obstruction theory and includes dimension estimates of various Hilbert schemes. For example, it is shown that most standard determinantal subschemes of codimension $3$ are unobstructed, and the dimensions of their components in the corresponding Hilbert schemes are computed.
Recent Progress In Homotopy Theory
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Author : Donald M. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Recent Progress In Homotopy Theory written by Donald M. Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion
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Author : Alexander Fel'shtyn
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion written by Alexander Fel'shtyn and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.