Locally Semialgebraic Spaces
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Locally Semialgebraic Spaces
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Author : Hans Delfs
language : en
Publisher: Springer
Release Date : 2006-11-14
Locally Semialgebraic Spaces written by Hans Delfs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Homology Of Locally Semialgebraic Spaces
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Author : Hans Delfs
language : en
Publisher: Springer
Release Date : 2006-11-14
Homology Of Locally Semialgebraic Spaces written by Hans Delfs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Locally semialgebraic spaces serve as an appropriate framework for studying the topological properties of varieties and semialgebraic sets over a real closed field. This book contributes to the fundamental theory of semialgebraic topology and falls into two main parts. The first dealswith sheaves and their cohomology on spaces which locally look like a constructible subset of a real spectrum. Topics like families of support, homotopy, acyclic sheaves, base-change theorems and cohomological dimension are considered. In the second part a homology theory for locally complete locally semialgebraic spaces over a real closed field is developed, the semialgebraic analogue of classical Bore-Moore-homology. Topics include fundamental classes of manifolds and varieties, Poincare duality, extensions of the base field and a comparison with the classical theory. Applying semialgebraic Borel-Moore-homology, a semialgebraic ("topological") approach to intersection theory on varieties over an algebraically closed field of characteristic zero is given. The book is addressed to researchers and advanced students in real algebraic geometry and related areas.
Locally Semialgebraic Spaces
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Author : Hans Delfs
language : en
Publisher:
Release Date : 2014-01-15
Locally Semialgebraic Spaces written by Hans Delfs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Weakly Semialgebraic Spaces
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Author : Manfred Knebusch
language : en
Publisher: Springer
Release Date : 2006-11-14
Weakly Semialgebraic Spaces written by Manfred Knebusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic spaces over R was studied. The category WSA(R) of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA(R) as a full subcategory. The book provides ample evidence that WSA(R) is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA(R) seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA(R) and WSA(R) as the full subcategory SA(R) of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA(R) with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology.
A Glimpse Into Geometric Representation Theory
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Author : Mahir Bilen Can
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-07
A Glimpse Into Geometric Representation Theory written by Mahir Bilen Can 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 2024-08-07 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Combinatorial and Geometric Representation Theory, held virtually on November 20–21, 2021. The articles offer an engaging look into recent advancements in geometric representation theory. Despite diverse subject matters, a common thread uniting the articles of this volume is the power of geometric methods. The authors explore the following five contemporary topics in geometric representation theory: equivariant motivic Chern classes; equivariant Hirzebruch classes and equivariant Chern-Schwartz-MacPherson classes of Schubert cells; locally semialgebraic spaces, Nash manifolds, and their superspace counterparts; support varieties of Lie superalgebras; wreath Macdonald polynomials; and equivariant extensions and solutions of the Deligne-Simpson problem. Each article provides a well-structured overview of its topic, highlighting the emerging theories developed by the authors and their colleagues.
The Basic Theory Of Real Closed Spaces
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Author : Niels Schwartz
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
The Basic Theory Of Real Closed Spaces written by Niels Schwartz 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 1989 with Mathematics categories.
Much in the same way as classical algebraic varieties are generalized by the theory of schemes, locally semi-algebraic spaces are generalized by a class of locally ringed spaces, called real closed spaces. The underlying spaces of affine real closed spaces are real spectra of rings, the structure sheaves are called real closed sheaves. With these spaces a theory can be developed which is very similar to the theory of schemes. There is a natural functor from the category of semi-algebraic spaces to the category of real closed spaces. Via this functor properties of semi-algebraic spaces and their corresponding real closed spaces can be compared.
Real Algebraic Geometry
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Author : Michel Coste
language : en
Publisher: Springer
Release Date : 2006-11-15
Real Algebraic Geometry written by Michel Coste and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contributions by: S. Akbulut and H. King; C. Andradas and J. Ruiz; A. Borobia; L. Br|cker; G.W. Brumfield; A. Castilla; Z. Charzynski and P. Skibinski; M. Coste and M. Reguiat; A. Degtyarev; Z. Denkowska; J.-P. Francoise and F. Ronga; J.M. Gamboa and C. Ueno; D. Gondard- Cozette; I.V. Itenberg; P. Jaworski; A. Korchagin; T. Krasinksi and S. Spodzieja; K. Kurdyka; H. Lombardi; M. Marshall and L. Walter; V.F. Mazurovskii; G. Mikhalkin; T. Mostowski and E. Rannou; E.I. Shustin; N. Vorobjov.
Tame Topology And O Minimal Structures
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Author : Lou Van den Dries
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07
Tame Topology And O Minimal Structures written by Lou Van den Dries 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 1998-05-07 with Mathematics categories.
These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
Real And Etale Cohomology
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Author : Claus Scheiderer
language : en
Publisher: Springer
Release Date : 2006-11-15
Real And Etale Cohomology written by Claus Scheiderer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, étale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.
Topology Of Singular Spaces And Constructible Sheaves
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Author : Jörg Schürmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Topology Of Singular Spaces And Constructible Sheaves written by Jörg Schürmann 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.
Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.