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'.
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 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of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki,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.
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.
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.
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'.
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. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.