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

- 374 Want to read
- 21 Currently reading

Published
**2008** by Cambridge University Press in Cambridge .

Written in English

- Quadratic Forms,
- Cochain Complexes,
- Surgery (Topology),
- Topological manifolds

**Edition Notes**

Statement | A.A. Ranicki |

Series | Cambridge tracts in mathematics, Cambridge tracts in mathematics |

The Physical Object | |
---|---|

Pagination | p. cm. |

ID Numbers | |

Open Library | OL27015862M |

ISBN 10 | 0521055210 |

ISBN 10 | 9780521055215 |

OCLC/WorldCa | 190967385 |

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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 Algebraic L-theory and topological manifolds book and topological manifolds. [Andrew Ranicki] -- The Browder-Novikov-Sullivan-Wall surgery theory emerged in the s as the main 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 Algebraic L-theory and topological manifolds book 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 Algebraic L-theory and topological manifolds book 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 Algebraic L-theory and topological manifolds book 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 Algebraic L-theory and topological manifolds book (New York, Macmillan; London: Collier-Macmillan, c), Algebraic L-theory and topological manifolds book 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. 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.

In mathematics, the surgery structure set is the basic object in the study of manifolds which are homotopy equivalent to a closed manifold X. It is a concept which helps to answer the question whether two homotopy equivalent manifolds are diffeomorphic (or PL-homeomorphic or homeomorphic).There are different versions of the structure set depending on the category.

Read Now ?book= Algebraic L-theory and topological manifolds, Cambridge Tracts in MathematicsCUP () [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 inthe 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).

The AMS Bookstore is open, but rapid changes related to the spread of COVID may cause delays in delivery services for print products. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.

"Algebraic L-theory and Topological Manifolds" by Andrew A. Ranicki, Cambridge Tracts in Mathematics, vol. Cambridge Univ. Press,pp., Hardback, ISBN$ This book explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

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.

FRIEDHELM WALDHAUSEN, Algebraic ^-theory of topological spaces. I 35 J. ALEXANDER, P. CONNER and G. HAMRICK, Metabolic and hyperbolic forms 61 JEAN-CLAUDE HAUSMANN and PIERRE VOGEL, The plus construction and lifting maps from manifolds 67 Surgery and its Applications R.

JAMES MILGRAM, A survey of the classifying spaces. Vogell W. () The canonical involution on the algebraic K-theory of spaces. In: Madsen I.H., Oliver R.A. (eds) Algebraic Topology Aarhus 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. Abstract. We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite-dimensional CAT(0) by: Description: This book is an introduction to manifolds at the beginning graduate level.

It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. 3For example, my own work on the algebraic L-theory orientations of topological manifolds and bundles.

4The picture of an inﬂnite mapping telescope on page 34 is a rendering of the picture in the Russian edition. 5A man of the ﬂrst hour. Read Topological Spaces From Distance to Neighborhood Undergraduate Texts in Mathematics Ebook Free.

We prove the existence of download pdf map of spectra \(\tau _A:kA \rightarrow \ell A\) between connective topological K-theory and connective algebraic L-theory of a complex \(C^*\)-algebra A which is natural in A and compatible with multiplicative structures.

We determine its effect on homotopy groups and as a consequence obtain a natural equivalence \(KA\left[ Cited by: 3.A Ebook Ranicki, Algebraic L{theory and topological manifolds, Cambridge Tracts in MathematicsCambridge University Press, Cambridge () MR MR C P Rourke, The Hauptvermutung according to Casson and Sullivan, from: "The Hauptvermutung book", K|Monogr.

Math. 1, Kluwer Acad. Publ., Dordrecht () { MR