Description

These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'. The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These 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. The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These 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. 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of Novikov's original 1970 statement of his conjecture • An annotated problem list • The texts of several important unpublished classic papers by Milnor, Browder, and Kasparov • Research/survey papers on the Novikov Conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg. 1. Homotopy type of differentiable manifolds William Browder; 2. A history and survey of the Novikov conjecture S. C. Ferry, A. RanickI and J. Rosenberg; 3. A coarse approach to the Novikov conjecture S. C. Ferry and Shmuel Weinberger; 4. Reflections on the Novikov conjecture Mikhael Gromov; 5. K-theory, group C*-algebras and higher signatures (Conspectus) Gennadi Kasparov; 6. On the Steenrod homology theory John Milnor; 7. Controlled Fredholm Representations A. S. Mishchenko; 8. Assembly maps in bordism-type theories Frank Quin; 9. On the Novikov conjecture Andrew Ranicki. 'These proceedings will be useful for all who are interested in related fields of mathematics such as topology, geometry and analysis and especially for those who are attracted by problems related to the topology of manifolds.' European Mathematical Society Newsletter ' … this two volume collection ofers a very nice way to see both the historical development and the current activities in the field.' Monatshefte für Mathematik