Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | The Novikov Conjecture - Geometry and Algebra

The Novikov Conjecture

Geometry and Algebra

Series: Oberwolfach Seminars, Vol. 33

Kreck, Matthias, Lück, Wolfgang

2005, XV, 266 p.

A product of Birkhäuser Basel
Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-7643-7315-3

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-7643-7141-8

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

Manifolds are the central geometric objects in modern mathematics. An attempt to understand the nature of manifolds leads to many interesting questions. One of the most obvious questions is the following. Let M and N be manifolds: how can we decide whether M and N are ho- topy equivalent or homeomorphic or di?eomorphic (if the manifolds are smooth)? The prototype of a beautiful answer is given by the Poincar´ e Conjecture. If n N is S ,the n-dimensional sphere, and M is an arbitrary closed manifold, then n it is easy to decide whether M is homotopy equivalent to S . Thisisthecaseif and only if M is simply connected (assumingn> 1, the case n = 1 is trivial since 1 every closed connected 1-dimensional manifold is di?eomorphic toS ) and has the n homology of S . The Poincar´eConjecture states that this is also su?cient for the n existenceof ahomeomorphism fromM toS . For n = 2this followsfromthewe- known classi?cation of surfaces. Forn> 4 this was proved by Smale and Newman in the 1960s, Freedman solved the case in n = 4 in 1982 and recently Perelman announced a proof for n = 3, but this proof has still to be checked thoroughly by the experts. In the smooth category it is not true that manifolds homotopy n equivalent to S are di?eomorphic. The ?rst examples were published by Milnor in 1956 and together with Kervaire he analyzed the situation systematically in the 1960s.

Content Level » Research

Keywords » Algebraische Topologie - Characteristic class - Differentialtopologie - Invariantentheorie - homology - manifold - vector bundle

Related subjects » Birkhäuser Mathematics

Table of contents 

A Motivating Problem.- to the Novikov and the Borel Conjecture.- Normal Bordism Groups.- The Signature.- The Signature Theorem and the Novikov Conjecture.- The Projective Class Group and the Whitehead Group.- Whitehead Torsion.- The Statement and Consequences of the s-Cobordism Theorem.- Sketch of the Proof of the s-Cobordism Theorem.- From the Novikov Conjecture to Surgery.- Surgery Below the Middle Dimension I: An Example.- Surgery Below the Middle Dimension II: Systematically.- Surgery in the Middle Dimension I.- Surgery in the Middle Dimension II.- Surgery in the Middle Dimension III.- An Assembly Map.- The Novikov Conjecture for ?n.- Poincaré Duality and Algebraic L-Groups.- Spectra.- Classifying Spaces of Families.- Equivariant Homology Theories and the Meta-Conjecture.- The Farrell-Jones Conjecture.- The Baum-Connes Conjecture.- Relating the Novikov, the Farrell-Jones and the Baum-Connes Conjectures.- Miscellaneous.- Exercises.- Hints to the Solutions of the Exercises.

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebraic Topology.

Additional information