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Monday, August 3, 2020 | History

1 edition of Geometry of Vector Sheaves found in the catalog.

Geometry of Vector Sheaves

An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications

by Anastasios Mallios

  • 262 Want to read
  • 4 Currently reading

Published by Springer Netherlands in Dordrecht .
Written in English

    Subjects:
  • Functional analysis,
  • Harmonic analysis,
  • Mathematics,
  • Global differential geometry,
  • Algebraic topology,
  • Global analysis

  • About the Edition

    This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (`differential spaces"), to non-linear PDEs (generalised functions). Thus, more general applications, which are no longer `smooth" in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the `world around us is far from being smooth enough". Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.

    Edition Notes

    Statementby Anastasios Mallios
    SeriesMathematics and Its Applications -- 439, Mathematics and Its Applications -- 439
    Classifications
    LC ClassificationsQA641-670
    The Physical Object
    Format[electronic resource] :
    Pagination1 online resource (xlii, 882 p.)
    Number of Pages882
    ID Numbers
    Open LibraryOL27041071M
    ISBN 109401061025, 9401150060
    ISBN 109789401061025, 9789401150064
    OCLC/WorldCa851375599

      This inspiring book belongs in the hands of any mathematician who has ever encountered a vector bundle on an algebraic variety.' Max Lieblich, University of Washington 'This book fills a great need: it is almost the only place the foundations of the moduli theory of sheaves on algebraic varieties appears in any kind of expository : Daniel Huybrechts. Buy Geometry of Vector Sheaves: An Axiomatic Approach To Differential Geometry Volume Ii: Geometry. Examples And Applications (Mathematics And Its Applications (Closed)) Softcover reprint of the original 1st ed. by Mallios, Anastasios (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible : Anastasios Mallios.

    Get this from a library! Geometry of vector sheaves: an axiomatic approach to differential geometry. [Anastasios Mallios]. Vector bundles and locally free sheaves Quasicoherent sheaves Characterizing quasicoherence using the distinguished affine base Quasicoherent sheaves form an abelian category Module-like constructions Finite type and coherent sheaves Pleasant properties of finite type and.

    Vector geometry / Gilbert de B. Robinson. — Dover ed. p. cm. Originally published: Boston: Allyn and Bacon, Summary: “This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. It is the result of several years of teaching and of learning from. Get this from a library! Geometry of Vector Sheaves: an Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications. [Anastasios Mallios] -- This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus.


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Geometry of Vector Sheaves by Anastasios Mallios Download PDF EPUB FB2

Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications (Mathematics and Its Applications) (Vol 1) th Edition.

Find all the books, read about the author, and by: Geometry of Vector Sheaves: An Axiomatic Approach To Differential Geometry Volume Ii: Geometry. Examples And Applications (Mathematics And Its Applications (Closed)) Softcover reprint of the original 1st ed.

EditionCited by: About this book This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (C INFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is : Springer Netherlands. Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry, Anastasios Mallios, ISBNVolume 1 of Geometry of vector sheaves, Anastasios Mallios an.

Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry, Volume 2. Geometry of Vector Sheaves.: Anastasios Mallios. Springer Science & Business Media, - Geometry, Differential - pages. 0 Reviews. This two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus.

Geometry of Vector Sheaves. An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications. Authors. (view affiliations) Anastasios Mallios. Book. 26 Citations. "The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves.

It is designed also as a reference book with detailed expositions and complete and self-contained proofs." (Witold Mozgawa, Zentralblatt MATH, Vol. ). Geometry of Vector Sheaves. A-connections. Authors; Authors and affiliations; in particular, vector sheaves and their algebra (linear and multilinear) and/or sheaf cohomology, to the extent that these issues have been developed in the preceding chapters.

Nontheless, as we shall realize through the succeeding discussion, several fundamental Cited by: 6. Key words: sheaves and presheaves, connections. 1 Introduction In [3] and [4], A. Mallios has considered ^-connections on vector sheaves.

Roughly speaking, a vector sheaf € is a locally free.A-module of finite rank over a topological space X, where A is. 4 Vector Geometry Vectors and Lines. In this chapter we study the geometry of 3-dimensional space. We view a point in 3-space as an arrow from the origin to that point.

Doing so provides a “picture” of the point that is truly worth a thousand words. Vectors in. Introduce a coordinate system in 3-dimensional space in the usual way. Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry.

Examples and Applications | Anastasios Mallios (auth.) | download | B–OK. Download books for free. Find books. "The book provides an accessible, well-written monograph devoted to the theory of principal sheaves and their connections in the setting initiated by, Geometry of vector sheaves.

It is designed also as a reference book with detailed expositions and complete and self-contained proofs." (Witold Mozgawa, Zentralblatt MATH, Vol. )Price: $ It is the definitive reference for the important topics of vector bundles, coherent sheaves, moduli spaces and geometric invariant theory; perfect as both an introduction to these subjects for beginners, and as a reference book for : Daniel Huybrechts, Manfred Lehn.

Geometry of Vector Sheaves: Vector Sheaves - General Theory v. 1 by Anastasios Mallios,available at Book Depository with free delivery : Anastasios Mallios. It is the goal of this book to share this “secret” geometry of schemes.

Chapters I and II, with the beginning of Chapter III, form a rapid intro-duction to basic definitions, with plenty of concrete instances worked out to give readers experience and confidence with important families of Size: 1MB.

The topic of this book is the theory of semistable coherent sheaves on a smooth algebraic surface and of moduli spaces of such sheaves. The content ranges from the definition of a semistable sheaf and its basic properties over the construction of moduli spaces to the birational geometry of these moduli spaces.

Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry. Examples and Applications (Paperback) by Anastasios Mallios and a great selection of related books, art and collectibles available now at : Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry Volume II: Geometry.

Examples and Applications (Mathematics and Its Applications) (Vol 1) () by Mallios, Anastasios and a great selection of similar New, Used and Collectible Books available now at.

The content ranges from the definition of a semistable sheaf and its basic properties over the construction of moduli spaces to the bira- tional geometry of these moduli spaces.

The book is intended for readers with some back- ground in Algebraic Geometry, as. v.1 Geometry of Vector Sheaves Vector Sheaves - General Theory AND Antal komponenter 1 Komponenter 1 Hardback ISBN.

This text is part of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus.

Here, the sheaf-theoretic character is emphasized.Contents Preface ix 1 Sheaves and all that 1 Sheaves 2 Sheaves and morphisms.8. Line sheaves over the spectrum of a geometric topological algebra 8.(a).

Morphisms of short exact exponential sheaf sequences (contn'd) 9. Frobenius integrability condition (contn'd) Flat A-vector bundles vis-a-vis to 5-flatness of the associated vector sheaves (a). 3-flatness of A-vector bundles Watts File Size: KB.