K-Monographs in Mathematics – serie
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13 produkter
13 produkter
Del 1 - K-Monographs in Mathematics
Hauptvermutung Book
A Collection of Papers on the Topology of Manifolds
Inbunden, Engelska, 1996
1 702 kr
Skickas inom 10-15 vardagar
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. Then, the development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960s. This volume brings together the original papers of Casson and Sullivan (1967), and the `Princeton Notes on the Hauptvermutung' of Armstrong, Rourke and Cooke (1968/1972). They include several results which have become part of mathematical folklore, but of which proofs had never been published. The material is complemented by an introduction on the Hauptvermutung and an account of recent developments in the area. Also, references have been updated wherever possible.
537 kr
Skickas inom 10-15 vardagar
This text presents a theory of filtrations on associative rings, combining techniques stemming from number theory related to valuations, with facts originating in the study of rings of differential operators on varieties. It deals with the homological algebra part of the theory via an innovative use of graded ring theory applied to the Rees ring of a filtration. This leads to an approach to extensions of valuations, regularity conditions on noncommutative algebras, and geometric aspects of rings of differential operators, and provides new applications related to deformations of algebras, gauge algebras and other physics-related objects. This volume should be of interest to graduate students and researchers in different fields of mathematics and mathematical physics.
Del 3 - K-Monographs in Mathematics
Non-Commutative Valuation Rings and Semi-Hereditary Orders
Inbunden, Engelska, 1997
1 066 kr
Skickas inom 10-15 vardagar
This is a self-contained summary of non-Noetherian orders in a simple Artinian ring, a subject in which much progress has been made in the last decade. The contents of the book are mainly Dubrovin valuation rings and semi-hereditary orders, including Prufer and semi-local Bezout orders, which are considered, in a sense, as global theories of Dubrovin valuation rings. These are then developed further, and applied to give some examples such as Dubrovin valuation rings in crossed product algebras, semi-hereditary maximal order in certain matrix rings, and the idealizers of semi-hereditary orders and Henselization of Bezout orders.
Del 5 - K-Monographs in Mathematics
Classical and Involutive Invariants of Krull Domains
Inbunden, Engelska, 1999
1 066 kr
Skickas inom 10-15 vardagar
This monograph is devoted to Krull domains and its invariants. The book shows how a serious study of invariants of Krull domains necessitates input from various fields of mathematics, including rings and module theory, commutative algebra, K-theory, cohomology theory, localization theory and algebraic geometry. About half of the book is dedicated to so-called involutive invariants, such as the involutive Brauer group. The work presents a large quantity of results previously scattered throughout the literature. This volume is a first introduction to this rapidly developing subject, but will also be useful as a reference work, both to students at graduate and postgraduate levels and to researchers in commutative rings and algebra, algebraic K-theory, algebraic geometry, and associative rings.
537 kr
Skickas inom 10-15 vardagar
This text deals with algebraic topology, homotopy theory and simple homotopy theory of infinite CW-complexes with ends. The homotopy theory is approached without the rather sophisticated notion of pro-category. Spaces spherical objects of CW-complexes in the category of spaces with ends, and all arguments refer directly to this category. In this way, infinite homotopy theory is presented as a natural extension of classical homotopy theory. In particular, this book introduces the construction of the proper groupoid of a space with ends and then the cohomology with local coefficients is defined by the enveloping ringoid of the proper fundamental groupoid. This volume should be of interest to researchers whose work involves algebraic topology, category theory, homological algebra, general topology, manifolds, and cell complexes.
Del 4 - K-Monographs in Mathematics
Brauer Groups, Hopf Algebras and Galois Theory
Häftad, Engelska, 2002
537 kr
Skickas inom 10-15 vardagar
This volume is devoted to the Brauer group of a commutative ring and related invariants. Part one presents a self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and etale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part two presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in part one is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in part three. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph.
537 kr
Skickas inom 10-15 vardagar
This text provides an overview of some of the most active topics in the theory of transformation groups over the latter part of the 20th century and stresses advances obtained since around 1990. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semi-algebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into 15 articles and should be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.
Del 1 - K-Monographs in Mathematics
Hauptvermutung Book
A Collection of Papers on the Topology of Manifolds
Häftad, Engelska, 2010
1 711 kr
Skickas inom 10-15 vardagar
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that further development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. Then, the development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960s. Up to now, the published record of the Hauptvermutung has been incomplete. This volume brings together the original papers of Casson and Sullivan (1967), and the 'Princeton Notes on the Hauptvermutung' of Armstrong, Rourke and Cooke (1968/1972). They include several results which have become part of mathematical folklore, but of which proofs had never been published.The material is complemented by an introduction on the Hauptvermutung and an account of recent developments in the area. Also, references have been updated wherever possible. Audience: This book will be valuable to all mathematicians interested in the topology of manifolds, geometry, and differential geometry.
539 kr
Skickas inom 10-15 vardagar
This book is the first to present a complete theory of filtrations on associative rings, combining techniques stemming from number theory related to valuations, with facts originating in the study of rings of differential operators on varieties. It deals with the homological algebra part of the theory via an innovative use of graded ring theory applied to the Rees ring of a filtration. This leads to a completely new approach to extensions of valuations, regularity conditions on noncommutative algebras, and geometric aspects of rings of differential operators, and provides new applications related to deformations of algebras, gauge algebras and other physics-related objects. Audience: This volume will be of interest to graduate students and researchers in different fields of mathematics and mathematical physics.
Del 3 - K-Monographs in Mathematics
Non-Commutative Valuation Rings and Semi-Hereditary Orders
Häftad, Engelska, 2010
1 072 kr
Skickas inom 10-15 vardagar
This is the first self-contained summary of non-Noetherian orders in a simple Artinian ring, a subject in which much progress has been made in the last decade. The contents of the book are mainly Dubrovin valuation rings and semi-hereditary orders, including Prufer and semi-local Bezout orders, which are considered, in a sense, as global theories of Dubrovin valuation rings. These are then developed further, and applied to give some examples such as Dubrovin valuation rings in crossed product algebras, semi-hereditary maximal order in certain matrix rings, and the idealizers of semi-hereditary orders and Henselization of Bezout orders. Audience: This volume will be of interest to researchers and graduate students whose work involves non-commutative ring theory and module theory.
539 kr
Skickas inom 10-15 vardagar
This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.
539 kr
Skickas inom 10-15 vardagar
Compactness in topology and finite generation in algebra are nice properties to start with. However, the study of compact spaces leads naturally to non-compact spaces and infinitely generated chain complexes; a classical example is the theory of covering spaces. In handling non-compact spaces we must take into account the infinity behaviour of such spaces. This necessitates modifying the usual topological and algebraic cate gories to obtain "proper" categories in which objects are equipped with a "topologized infinity" and in which morphisms are compatible with the topology at infinity. The origins of proper (topological) category theory go back to 1923, when Kere kjart6 [VT] established the classification of non-compact surfaces by adding to orien tability and genus a new invariant, consisting of a set of "ideal points" at infinity. Later, Freudenthal [ETR] gave a rigorous treatment of the topology of "ideal points" by introducing the space of "ends" of a non-compact space. In spite of its early ap pearance, proper category theory was not recognized as a distinct area of topology until the late 1960's with the work of Siebenmann [OFB], [IS], [DES] on non-compact manifolds.
Del 5 - K-Monographs in Mathematics
Classical and Involutive Invariants of Krull Domains
Häftad, Engelska, 2013
1 072 kr
Skickas inom 10-15 vardagar
Just suppose, for a moment, that all rings of integers in algebraic number fields were unique factorization domains, then it would be fairly easy to produce a proof of Fermat's Last Theorem, fitting, say, in the margin of this page. Unfortunately however, rings of integers are not that nice in general, so that, for centuries, math ematicians had to search for alternative proofs, a quest which culminated finally in Wiles' marvelous results - but this is history. The fact remains that modern algebraic number theory really started off with in vestigating the problem which rings of integers actually are unique factorization domains. The best approach to this question is, of course, through the general the ory of Dedekind rings, using the full power of their class group, whose vanishing is, by its very definition, equivalent to the unique factorization property. Using the fact that a Dedekind ring is essentially just a one-dimensional global version of discrete valuation rings, one easily verifies that the class group of a Dedekind ring coincides with its Picard group, thus making it into a nice, functorial invariant, which may be studied and calculated through algebraic, geometric and co homological methods. In view of the success of the use of the class group within the framework of Dedekind rings, one may wonder whether it may be applied in other contexts as well. However, for more general rings, even the definition of the class group itself causes problems.