Last edited by Yozshuzshura
Saturday, August 1, 2020 | History

7 edition of The Novikov Conjecture found in the catalog.

The Novikov Conjecture

Geometry and Algebra (Oberwolfach Seminars)

by Matthias Kreck

  • 326 Want to read
  • 35 Currently reading

Published by Birkhäuser Basel .
Written in English

    Subjects:
  • Geometry,
  • Mathematics,
  • Science/Mathematics,
  • Geometry - General,
  • Topology - General,
  • Mathematics / Topology,
  • Geometry - Algebraic

  • The Physical Object
    FormatPaperback
    Number of Pages266
    ID Numbers
    Open LibraryOL9090908M
    ISBN 103764371412
    ISBN 109783764371418

    Physicists have long known that some solutions to the theory of general relativity contain closed timelike curves —for example the Gödel metric. Novikov discussed the possibility of closed timelike curves (CTCs) in books he wrote in and , offering the opinion that only self-consistent trips back in time would be permitted. From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The bookBrand: Springer-Verlag Berlin Heidelberg.

    ISBN: OCLC Number: Description: xv, pages ; 24 cm. Contents: Motivating problem (K.) Introduction to the Novikov and the Borel conjecture (L.) Normal bordism groups (K.) signature (K.) signature theorem and the Novikov conjecture (K.) projective class group and the Whitehead group (L.) The Novikov conjecture: geometry and algebra. [Matthias Kreck; Wolfgang Lück] -- These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to .

    the Kaplansky Conjecture and the Kadison Conjecture on the non-existence of non-trivial idempotents in the group ring or the reduced group C -algebra of torsionfree groups, the Novikov Conjecture about the homotopy invariance of higher signatures, and the conjectures about the vanishing of the reducedFile Size: 2MB. Novikov's conjecture about the Riemann–Schottky problem (characterizing principally polarized abelian varieties that are the Jacobian of some algebraic curve) stated, essentially, that this was the case if and only if the corresponding theta function provided a solution to Alma mater: Moscow State University.


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The Novikov Conjecture by Matthias Kreck Download PDF EPUB FB2

The Novikov conjecture is the assertion that the assembly map is an isomorphism. Much of the first part of the book discusses how to make these notions meaningful and how to interpret them geometrically via the surgery obstruction by: : Novikov Conjectures, Index Theorems, and Rigidity: Volume 1: Oberwolfach (London Mathematical Society Lecture Note Series) (): Steven C.

This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture. Monatshefte für Mathematik “Overall, the book is very suitable both as an introduction and as a reference, and finds exactly the right balance between detail, comprehensiveness and length of the presentation.

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem.

Then an introduction to surgery theory and a version of the assembly map is presented. The Novikov conjecture, as well as the other, related, conjectures the book is concerned with (e.g. the Borel conjecture, the Baum-Connes conjecture) are. Search within book. Front Matter. Pages i-xv. PDF.

A Motivating Problem. Pages Introduction to the Novikov and the Borel Conjecture. Pages Normal Bordism Groups. Pages The Signature. Pages The Signature Theorem and the Novikov Conjecture.

Pages The Projective Class Group and the Whitehead Group. Pages The Novikov conjecture is an important problem in higher dimensional topology.

It asserts that the higher signatures of a compact smooth manifold are invariant under orientation preserving homotopy equivalences. In the past few decades, noncommu-tative geometry has The Novikov Conjecture book powerful techniques to study the Novikov : Jintao Deng.

Novikov-Shubin invariants { M. Gromov Re°ections on the Novikov conjecture { S. Hurder Exotic index theory and the Novikov conjecture { B.

Williams A proof of a conjecture of Lott Thursday, 9th September { M. Puschnigg Cyclic homology and the Novikov conjecture { U. Bunke Glueing problems for. The Novikov conjecture for compact aspherical manifolds follows from the Borel conjecture and Novikov’s theorem since for aspherical manfolds, the information about higher signatures is equivalent to that of rational Pontryagin classes.

The Novikov conjecture has inspired a lot of beautiful mathematics. We describe Novikov’s “higher signature conjecture,” which dates back to the late s, as well as many alternative formulations and related problems.

The Novikov Conjecture is perhaps the most important unsolved problem in high-dimensional manifold topology, but more importantly, variants and analogues permeate many other areas of mathematics, from geometry to Cited by: 6.

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem.

Then an introduction to surgery theory and a version of the assembly map is presented. Conjecture (Borel ()). Let Gbe any discrete group.

Any two closed manifolds of the homotopy type of BGare homeomorphic. This is an analogue of the Poincar e conjecture for aspherical manifolds (i.e., those with contractible universal covering space). The Novikov conjecture is a step towards this conjecture, from the point of.

subject of \Novikov conjectures, index theorems and rigidity." The aim of the meeting was to examine the Novikov conjecture, one of the central problems of the topology of manifolds, along with the vast assortment of reflnements, generalizations, and analogues of the conjecture which have proliferated over the last 25 years.

Book description The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds.

Open Library is an open, editable library catalog, building towards a web page for every book ever published. The Novikov Conjecture by Matthias Kreck,Wolfgang L.

Ck,Springer edition, paperback. From the reviews: This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture.

Monatshefte fur Mathematik "Overall, the book is very suitable both as an introduction and as a reference, and finds exactly the right balance between detail, comprehensiveness and length of the presentation.

By Matthias Kreck and Wolfgang Lück: pp., € (CHF), isbn 3‐‐‐2 (Birkhäuser, Basel, ).Author: Andrew Ranicki. For astrophysicist Igor Novikov's conjecture regarding time travel, see Novikov self-consistency principle.

The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold.

For a copy of Novikov’s original formulation oftheconjectureinRussian, aswellasanEnglishtranslation,thereadercanconsult [10, x11] or else x2 of \A history and survey of the Novikov Conjecture," in [4], by Steve Ferry, Andrew Ranicki, and this reviewer.

What has made the Novikov Conjecture so fascinating, and so central to con. This bibliography is based on the one in "A history and survey of the Novikov Conjecture" by Steve Ferry, Andrew Ranicki, and Jonathan Rosenberg. The original version appeared in volume 1 of "Novikov Conjectures, Index Theorems and Rigidity" (listed below under.

Manifold aspects of the Novikov Conjecture James F. Davis§ Let L M 2 H4§(M;Q) be the Hirzebruch L-class of an oriented manifold M.

Let Bº (or K(º,1)) denote any aspherical space with fundamental group º. (A space is aspherical if it has a contractible universal cover.)File Size: KB.Big picture of the Novikov Conjecture. The Novikov Conjec-ture (NC) states that the higher signatures of a manifold are homotopy invariant.

The higher signatures are the rational numbers of the type hL(M)∪ρ∗ M (x),[M]i, where [M] is the fundamental class of a manifold M, L is the Hirzebruch class, Γ = π 1(M), ρ M: M → BΓ = K(Γ,1).Another good survey is by S.

Weinberger, Aspects of the Novikov Conjecture, Contemp. Math. (), The recent book by F.T. Farrell, Surgical methods in rigidity, Tata Institute lecture notes (), is very readable and gets to recent results in just 60 pages.