Cover of: Exact sequences in the algebraic theory of surgery | A. Ranicki

Exact sequences in the algebraic theory of surgery

  • 863 Pages
  • 3.85 MB
  • 1477 Downloads
  • English
by
Princeton University Press , Princeton, N.J
Surgery (Topology), Sequences (Mathema
Statementby Andrew Ranicki.
SeriesMathematical notes -- 26, Mathematical notes (Princeton University Press) -- 26.
Classifications
LC ClassificationsQA613.658
The Physical Object
Pagination863p. ;
ID Numbers
Open LibraryOL21623661M
ISBN 100691082766

Surgery theory then attempts to find out if a Poincare complex X is homotopy equivalent to a manifold, by computing the topological structure set in terms of the algebraic topology of X. One approach to deciding if a Poincare complex is homotopy equivalent to a manifold is due to the mathematicians Felix Browder, S.P.

Novikov, C.T.C Wall, and Dennis by: The algebraic L-theory exact sequences are developed in SS, and the algebraic theory of codimension q surgery is developed in 7.

One of the principal aims of surgery theory is to classify the homotopy types of manifolds using tools from algebra and topology. The algebraic approach is emphasized in this book, and it gives the reader a good overview of the subject, as it was known at the time of publication.

M and the algebraic L-theory of quadratic forms over the fundamental group ring Z[ˇ1(M)]. The surgery exact sequence is stated in Chapter 1, and nally proved in Chapter Along the way, there are basic treatments of Morse theory, embeddings and immersions.

Enough machinery is developed to prove the main result of surgery theory: the surgery exact sequence computing the structure set of a differentiable manifold M of dimension > 5 in terms of the topological K-theory of vector bundles over M and the algebraic L-theory of quadratic forms over the fundamental group ring Z[ 1(M)].

The surgery. Cite this chapter as: Gabriel P., Zisman M. () Exact Sequences of Algebraic Topology. In: Calculus of Fractions and Homotopy Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol Author: Peter Gabriel, Michel Zisman. Topology Vol. 3, pp. Pergamon Press, Printed in Great Britain SOME EXACT SEQUENCES IN ALGEBRAIC K-THEORY ALEX HELLERt (Received 9 October ) INTRODUCTION H.

Bass [1] and I. Reiner and the author [4] have introduced exact sequences connecting the groups Ko, Kl of the so-called algebraic IC by: An algebraic theory of surgery on chain complexes with an abstract Poincare duality should be a 'simple and satisfactory algebraic version of the whole setup' to quote § 17G of the book of Wall.

1 "The total surgery obstruction" paper. 2 "Exact sequences in the algebraic theory of surgery" book. 3 "Algebraic L-theory and topological manifolds" book. 4 "The total surgery obstruction" MPIM lecture.

D. Quillen 1: Higher K-theory for categories with exact sequences, to appear in the procedings of the June Oxford symposium "New developments in topology". Google Scholar —D. Quillen: On the cohomology and K-theory of the general linear groups over a Cited by: THE ALGEBRAIC THEORY OF SURGERY READING SEMINAR ARTHUR BARTELS, TIBOR MACKO Abstract.

The total surgery obstruction s(X) of a finite Poincar´e complex X of formal dimension n is an element of a certain abelian group Sn(X) with the property that s(X) = 0 if and only if X is homotopy equivalent to a closed n-dimensional topological manifold. Both the definition of s(X) and the proof of.

Exact Sequences in the Algebraic Theory of Surgery, by ANDREW RANICKI Existence and Regularity of Minimal Surfaces on Riemannian Manifolds, by Hardy Spaces on Homogenous Groups, by G. FOLUAND and E. STEIN. The techniques developed in these papers were then applied in 'Exact Sequences in the Algebraic Theory of Surgery' ([7]), section 7, to give a definition of the UNil groups independent of the Author: Andrew Ranicki.

Exact sequences in the algebraic theory of surgery Add library to Favorites Please choose whether or not you want other users to be able to see on your profile that this library is a favorite of yours.

Algebraic number theory involves using techniques from (mostly commutative) algebra and finite group theory to gain a deeper understanding of number fields.

The main objects that we study in algebraic number theory are number fields, rings of integers of number fields, unit groups, ideal class groups,norms, traces,File Size: KB. MAPPING SURGERY TO ANALYSIS III The category C∗(X) was already defined in paper II (Definition ).

The category D∗(X) is a subcategory of the category A∗(X) defined in paper II.

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The quotient of a C∗-category by an ideal can be defined, and it is again a C∗ our categories we have the following important result. ( views) Algebraic and Geometric Surgery by Andrew Ranicki - Oxford University Press, Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more.

This book aims to be an entry point to surgery theory for a reader who already has some background in topology. Find helpful customer reviews and review ratings for Exact Sequences in the Algebraic Theory of Surgery.

(MN) (Mathematical Notes) at 4/5. Enough machinery is developed to prove the main result of surgery theory: the surgery exact sequence computing the structure set of a di erentiable manifold Mof dimension >5 in terms of the topological K-theory of vector bundles over M and the algebraic L-theory of quadratic forms over the fundamental group ring Z[ˇ 1(M)].

The surgery exact. Exact Sequences and Excision The Equivalence of Simplicial and Singular Homology stays well within the confines of pure algebraic topology. In a sense, the book could One can also find here the parts of the other two books in the sequence that are.

Even dimensional projective surgery groups of finite groups. Pages Kolster, Manfred. Preview Buy Chap95 € Exact sequences for locally free class groups. Pages Matchett, Andrew Algebraic K — Theory Book Subtitle Proceedings of a Conference Held at Oberwolfach, June Part II.

Description Exact sequences in the algebraic theory of surgery PDF

Find link is a tool written by Edward Betts. searching for Algebraic theory found ( total) alternate case: algebraic theory Algebraic signal processing (68 words) exact match in snippet view article find links to article In the algebraic theory of linear signal processing, a set of filters is treated as an algebra and a set of signals is treated as a module and the z-transform.

For an introduction to K–theory the classical alternative to the first of the two preced-ing books is: • M Atiyah. K–Theory. Perseus, [Originally published by W.A. Benjamin in ] [$55] More Advanced Topics. Again listing my favorites first, we have: • A Hatcher.

Spectral Sequences in Algebraic Topology. Unfinished book File Size: 65KB. Algebraic number theory involves using techniques from (mostly commutative) algebra and nite group theory to gain a deeper understanding of the arithmetic of number elds and related objects (e.g., functions elds, elliptic curves, etc.).

The main objects that we study in this book. Abstract. Surgery theory investigates the homotopy types of manifolds, using a\ud combination of algebra and topology.

It is the aim of these notes to provide\ud an introduction to the more algebraic aspects of the theory, without losing\ud sight of the geometric motivationAuthor: Andrew Ranicki.

The exact sequence. is important in many branches of mathematics, and is called a short exact sequence. This means that is a monomorphism, is an epimorphism, and that in.

As an example of a short exact sequence of abelian groups, we. The L-theory exact sequences of Theorem for an injective Ore localization A σ − 1 A (which is flat and hence stably flat) were obtained in Ranicki.

The quadratic L-theory exact sequence of (i) for arbitrary injective A σ − 1 A was obtained by Vogel. The symmetric L-theory exact sequence Author: Andrew Ranicki.

Five years ago, I taught a one-quarter course in homological algebra. I discovered that there was no book which was really suitable as a text for such a short course, so I decided to write one. The point was to cover both Ext and Tor early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions.

Details Exact sequences in the algebraic theory of surgery PDF

In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension >.

The localization exact sequences of algebraic K- and L-theory also hold in the noncommutative case. This chapter deals with K-theory, and L-theory will be considered in Chap.

ViewAuthor: Andrew Ranicki. Differential Graded Algebra. This note covers the following topics: Conventions, Differential graded algebras, Differential graded modules, The homotopy category, Cones, Admissible short exact sequences, Distinguished triangles, Cones and distinguished triangles, The homotopy category is triangulated, Projective modules over algebras, Injective modules over algebras, P-resolutions, I.Introduction To Algebraic Topology And Algebraic Geometry.

This note provides an introduction to algebraic geometry for students with an education in theoretical physics, to help them to master the basic algebraic geometric tools necessary for doing research in algebraically integrable systems and in the geometry of quantum eld theory and string theory.Long exact sequences associated to pairs 65 3.

Long exact sequences associated to fibrations 66 Textbooks in algebraic topology and homotopy theory CONTENTS ix 3. Books on CW complexes 4. Differential forms and Morse theory 5.

Equivariant algebraic topology 6. Category theory and homological algebra 7. Simplicial sets File Size: 1MB.