Homological And Homotopical Aspects Of Torsion Theories
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Homological And Homotopical Aspects Of Torsion Theories
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Author : Apostolos Beligiannis
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Homological And Homotopical Aspects Of Torsion Theories written by Apostolos Beligiannis 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 2007 with Mathematics categories.
In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories.
Homological And Homotopical Aspects Of Torsion Theories
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Author : Apostolos Beligiannis
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Homological And Homotopical Aspects Of Torsion Theories written by Apostolos Beligiannis 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 2007 with Mathematics categories.
In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along these lines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
On The Theory And Applications Of Differential Torsion Products
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Author : V. K. A. M. Gugenheim
language : en
Publisher: American Mathematical Soc.
Release Date : 1974
On The Theory And Applications Of Differential Torsion Products written by V. K. A. M. Gugenheim 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 1974 with Mathematics categories.
A new approach to differential homological algebra is developed, one which exploits more general types of resolutions than the bicomplexes used traditionally. An example of such a generalized resolution is exhibited and is used to prove that the differential torsion product reduces to the classical torsion product in favorable cases. This result is used to compute the cohomology of various spaces. The paper also includes proofs (within the new framework) of the results of Eilenberg and Moore which relate differential torsion products to the homology and cohomology of spaces, and a discussion of the relationship between differential torsion products and matric Massey products.
Interactions Between Homotopy Theory And Algebra
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Author : Luchezar L. Avramov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Interactions Between Homotopy Theory And Algebra written by Luchezar L. Avramov 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 2007 with Mathematics categories.
This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
Proper Equivariant Stable Homotopy Theory
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Author : Dieter Degrijse
language : en
Publisher: American Mathematical Society
Release Date : 2023-09-15
Proper Equivariant Stable Homotopy Theory written by Dieter Degrijse and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-15 with Mathematics categories.
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Purity Spectra And Localisation
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Author : Mike Prest
language : en
Publisher: Cambridge University Press
Release Date : 2009-06-04
Purity Spectra And Localisation written by Mike Prest 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 2009-06-04 with Mathematics categories.
A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum. It may be used as an introductory graduate-level text, providing relevant background material and a wealth of illustrated examples. An extensive index and thorough referencing also make this book an ideal reference.
Surveys In Representation Theory Of Algebras
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Author : Alex Martsinkovsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-12
Surveys In Representation Theory Of Algebras written by Alex Martsinkovsky 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 2018-09-12 with Representations of algebras categories.
This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.
Introduction To Combinatorial Torsions
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Author : Vladimir Turaev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To Combinatorial Torsions written by Vladimir Turaev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
Index Theory Eta Forms And Deligne Cohomology
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-03-06
Index Theory Eta Forms And Deligne Cohomology written by Ulrich Bunke 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 2009-03-06 with Mathematics categories.
This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions. The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds
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Author : Raphael Ponge
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds written by Raphael Ponge 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 2008 with Calculus categories.
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.