TY  - BOOK
AU  - Cavicchioli,Alberto
AU  - Cavicchioli,Alberto
AU  - Hegenbarth,Friedrich
AU  - Repovš,Dušan
TI  - Higher-Dimensional Generalized Manifolds: Surgery and Constructions
T2  - EMS Series of Lectures in Mathematics (ELM)
SN  - 9783037196564
PY  - 2016///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Topology
KW  - bicssc
KW  - Manifolds and cell complexes
KW  - msc
KW  - Category theory; homological algebra
KW  - $K$-theory
N1  - Restricted to subscribers
N2  - Generalized manifolds are a most fascinating subject to study. They were introduced in the 1930s, when topologists tried to detect topological manifolds among more general spaces (this is nowadays called the manifold recognition problem). As such, generalized manifolds have served to understand the nature of genuine manifolds. However, it soon became more important to study the category of generalized manifolds itself.   A breakthrough was made in the 1990s, when several topologists discovered a systematic way of constructing higher-dimensional generalized manifolds, based on advanced surgery techniques. In fact, the development of controlled surgery theory and the study of generalized manifolds developed in parallel. In this process, earlier studies of geometric surgery turned out to be very helpful.   Generalized manifolds will continue to be an attractive subject to study, for there remain several unsolved fundamental problems. Moreover, they hold promise for new research, e.g. for finding appropriate structures on these spaces which could bring to light geometric (or even analytic) aspects of higher-dimensional generalized manifolds.  This is the first book to systematically collect the most important material on higher-dimensional generalized manifolds and controlled surgery. It is self-contained and its extensive list of references reflects the historic development. The book is based on our graduate courses and seminars, as well as our talks given at various meetings, and is suitable for advanced graduate students and researchers in algebraic and geometric topology
UR  - https://doi.org/10.4171/156
UR  - http://www.ems-ph.org/img/books/cavicchioli_mini.jpg
ER  -