Novikov Conjectures, Index Theorems, and Rigidity: Volume 1: Oberwolfach 1993

ISBN-13: 9780521497961 / Angielski / Miękka / 1996 / 384 str.

Steven C. Ferry; Jonathan Rosenberg; Andrew Ranicki

Opis

The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes 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of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki,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. Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area.

Recenzje

' … 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

Spis treści

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.