Last edited by Faejar
Tuesday, May 19, 2020 | History

1 edition of Algebraic L-theory and topological manifolds found in the catalog.

# Algebraic L-theory and topological manifolds

## by Andrew Ranicki

Written in English

Subjects:
• Cochain Complexes,
• Surgery (Topology),
• Topological manifolds

• Edition Notes

The Physical Object ID Numbers Statement A.A. Ranicki Series Cambridge tracts in mathematics, Cambridge tracts in mathematics Pagination p. cm. Open Library OL27015862M ISBN 10 0521055210 ISBN 10 9780521055215 OCLC/WorldCa 190967385

Algebraic L-theory and topological manifolds, Cambridge Tracts in Mathematics , CUP () [23] (ed.), The Hauptvermutung Book, Papers in Author: Andrew Ranicki.   Archived. This topic is now archived and is closed to further replies. Algebraic Methods In Unstable Homotopy Theory. By Bo0mB0om, Decem in E-book - Kitap.

For a brief discussion of topology of manifolds which is the context for the conjectures, including more refined statements, see Shmuel Weinberger's review [Bull. Amer. Math. Soc. 33 (), pp. ] of the book by Andrew Ranicki, Algebraic L-theory and topological manifolds, Cambridge Tracts in Math., Vol. , Cambridge Univ. Press (). $\begingroup$ John Lee's book "Intro to Smooth Manifolds" is a classic with a nice section on DeRham theory (the cohomology of differential forms, dual to submanifolds by the pairing "integration"). Bott and Tu, "Differential Forms in Algebraic Topology" is a little more advanced, but well-written. Certainly take a look at it. This is the classic way to use duality to represent .

I used simplicial complexes of the Wikipedia kind in my CUP book Algebraic L-theory and Topological Manifolds to construct the algebraic L-theory assembly map. The construction was extended to $\Delta$-sets (in the sense of Rourke and Sanderson - not to be confused with Allen Hatcher's $\Delta$-complexes) in my joint paper with. Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in , the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier 3/5(1).

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### Algebraic L-theory and topological manifolds by Andrew Ranicki Download PDF EPUB FB2

ALGEBRAIC L-THEORY AND TOPOLOGICAL MANIFOLDS i University of Edinburgh This is the full text of the book published in as Volume of the Cambridge Tracts in Mathematics by the Cambridge University Press, with some corrections and additional material. The list of changes is maintained on my WWW Home Page.

The author calls the relationship between topological manifolds, Poincare spaces, local algebraic Poincare complexes, and global algebraic Poincare complexes a "fiber square" in the book. In analogy with hermitian K-theory, the quadratic L-groups were defined by the author in a previous work as cobordism of quadratic Poincare complexes over a Cited by: Find helpful customer reviews and review ratings for Algebraic L-theory and Topological Manifolds (Cambridge Tracts in Mathematics) at Read honest and 5/5(1).

Algebraic L theory and Topological Manifolds. Currently this section contains no detailed description for the page, will update this page soon. Algebraic L-theory and Topological Manifolds (Cambridge Tracts in Mathematics) Algorithms - ESA ' Second Annual European Symposium, Utrecht, The Netherlands, September 26 - 28, Proceedings (Lecture Notes in Computer Science).

pact di erentiable and PLmanifolds, and extended to topological manifolds by Kirby and Siebenmann. The term ‘algebraic L-theory’ was coined by Wall, to mean the algebraic K-theory of quadratic forms, alias hermitian K-theory. In the classical theory of quadratic forms the ground ring is a eld, or a ring of integers in an.

Algebraic L-theory and Topological Manifolds by A. Ranicki,available at Book Depository with free delivery worldwide. Get this from a library. Algebraic L̲-theory and topological manifolds. [Andrew Ranicki] -- The Browder-Novikov-Sullivan-Wall surgery theory emerged in the s as the Algebraic L-theory and topological manifolds book technique for classifying high-dimensional topological manifolds, using the algebraic L.

The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance of the higher signatures; any other formulation necessarily factors through this one.

Cambridge Tracts in Mathematics: Algebraic L-Theory and Topological Manifolds (Paperback). This book presents the definitive account of the applications of this algebra to the surgery classification of topological manifolds.

The central result is the identification of a manifold structure in the homotopy type of a Poincar&#; duality space with a local quadratic structure in the Price: \$ Algebraic L theory and Topological Manifolds [PDF p] The book is divided into two parts, called Algebra and Topology.

In principle, it is possible to start with the Introduction, and go on to the topology in Part II, referring back to Part I for novel algebraic concepts. Author(s): A. This book presents the definitive account of the applications of this algebra to the surgery classification of topological manifolds.

The central result is the identification of a manifold structure in the homotopy type of a Poincare duality space with a local quadratic structure in the chain homotopy type of the universal cover. dict the algebraic K-and L-theory of group rings and the topological K-theory of reduced group C -algebras.

These theories are of major interest for many reasons. For instance, the algebraic L-groups are the recipients for var-ious surgery obstructions and hence highly relevant for the classi cation of Size: 2MB. Algebraic Topology (c), by Allen Hatcher (PDF files with commentary at Cornell) Modern Algebraic Topology (New York, Macmillan; London: Collier-Macmillan, c), by D.

Bourgin (page images at HathiTrust) A Concise Course in Algebraic Topology (electronic edition, with errata corrected), by J. Peter May (PDF at Chicago).

Lower K and L Theory, London Mathematical Society Lecture Notes, Vol. Cambridge University Press. Algebraic L-Theory and Topological Manifolds', Cambridge Tracts in Mathematics Vol.Cambridge University Press, Algebraic and Geometric Surgery, Oxford University Press, High dimensional knot theory, Springer, Alma mater: University of Cambridge.

Filed under: Topological manifolds. The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (ca. ), ed. by Andrew Ranicki (PDF in the UK) Algebraic L-Theory and Topological Manifolds (electronic edition, ), by Andrew Ranicki (PDF in the UK) More items available under broader and related terms at left.

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. 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.

( views) Algebraic L-theory and Topological Manifolds by A. Ranicki - Cambridge University Press, Surgery theory expresses the manifold structure set in terms of the topological K-theory of vector bundles and the algebraic L-theory of quadratic forms.

While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading. This book is an introduction to surgery theory, the standard algebraic topology classification method for manifolds of dimension greater than 4.

It is aimed at those who have already been on a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra Author: Andrew Ranicki.

The structure space \mathcal{S}(M) of a closed topological m-manifold M classifies bundles whose fibers are closed m-manifolds equipped with a homotopy equivalence to M. The authors construct a highly connected map from \mathcal{S}(M) to a concoction of algebraic L-theory and algebraic K-theory spaces associated with M.and Cappell on the algebraic K- and L-theory of generalized free prod-ucts.

In a sense, this is more in the nature of an application of topology to noncommutative localization! But this algebra has in turn topological applications, since in dimensions >5 the surgery classiﬁcation of manifolds within a homotopy type reduces to algebra.

1.The main corollary is a functorial two-stage decomposition of F(V) for dim(V) > 5 which has the L-theory of the group Z/2 as one layer, and a form of unreduced homology of .