Novikov conjectures, index theorems and rigidity. Vol. 1 / edited by Steven C. Ferry, Andrew Ranicki, Jonathan Rosenberg.

"Outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September 1993"--Back cover

"Oberwolfach 1993."

Includes a reprint in Russian of Novikov's original 1970 statement of his conjecture.

Print version record.

Cover; Title; Copyright; Dedication; Contents; Contents, Volume 1; Contents, Volume 2; Preface; Programme of the Conference; Monday, 6th September; Tuesday, 7th September; Proper affine isometric actions of amenable groups, M.E. Bekka, P.-A. Cherix, and Alain Valette; Wednesday, 8th September; Thursday, 9th September; Friday, 10th September; Participant List from the Conference; Organizers:; Other participants; Bounded K-theory and the assembly map in algebraic K-theory, Gunnar Carlsson; A history and survey of the Novikov conjecture, StevenC . Ferry, And rewRanicki, and JonathanRosenberg

1. Precursors of the Novikov Conjecture2. The Original Statement of the Novikov Conjecture; 3. Work related to the Novikov Conjecture: The First12 Years or So; 4. Work related to the Novikov Conjecture: The Last 12Years or So, I: Homotopy Theory and Algebra; 5. Work related to the Novikov Conjecture: The Last 12Years or So, II: Geometric Topology; 6. Work related to the Novikov Conjecture: The Last 12Years or So, III: Elliptic Operators and Operator Algebras; Annotated Problem List; Proposed by M. Gromov; Proposed by C. Stark; Proposed by A. Ranicki; Proposed by S. Ferry and S. Weinberger

Proposed by M. RothenbergProposed by J. Rosenberg; Proposed by J. Davis; Proposed by J. Roe; Proposed by J. Cuntz and M. Puschnigg; Proposed by A. Valette; Proposed by S. Hurder; Proposed by F. Connolly; Proposed by T. Kozniewski; Proposed by M. Yan; Proposed by E, Pedersen; Proposed by B. Williams; Proposed by W. Liick; On the Steenrod homology theory (first distributed 1961), John Milnor; 1. The Uniqueness Theorem; 2. A continuity property of the Steenrod homology; 3. Axioms for cohomology; 4. Construction of a homology theory; Appendix. Derived functors of inverse limits.; References

Addendum (May 1995)Theorem 1.; Theorem 2.; Lemma 1; Lemma 2.; Lemma 3.; Lemma 4.; References; K-theory, group C*-algebras, and higher signatures (Conspectus) (first distributed 1981), Gennadi G. Kasparov; Preface; Introduction; 1. Notation; 2. The stabilization of Hilbert modules; 3. The technique of product-intersection; 4. K-bifunctor; 5. The reduction of G to the maximal compact subgroup; 6. C*-algebras of connected groups; 7. C*-algebras of discrete groups; On the rigidity of the index on open manifolds, Jiirgen Eichhorn; 8. Represent able K- functor and Poincare duality

9. Higher signaturesREFERENCES; A coarse approach to the Novikov conjecture, Steven C. Ferry and Shmuel Weinberger; 1. Background; Remarks on Steenrod homology, Steven C. Ferry; 2. The bounded category; 3. Topological invariance of rational Pontrjagin classes; 4. Application of the principle of descent to the NovikovConjecture; 5. Remarks on extensions; 6. Appendix; Remark; REFERENCES; Geometric reflections on the Novikov conjecture, Mikhael Gromov; Epsilon surgery theory, Steven C. Ferry and Erik K. Pedersen; Theorem (Vafa and Witten [VW]).; REFERENCES

The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September 1993, on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'. They are intended to give a snapshot of the status of work on the Novikov Conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry and analysis. Volume 1 contains: " A detailed historical survey and bibliography of the Novikov Conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; " An annotated problem list; " The texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and " Research/survey papers on the Novikov Conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg

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