LEADER 03523nam 22005055a 450 001 9910153273303321 005 20160524234501.0 010 $a3-03719-656-4 024 70$a10.4171/156 035 $a(CKB)3710000000961079 035 $a(CH-001817-3)203-160524 035 $a(PPN)193824116 035 $a(EXLCZ)993710000000961079 100 $a20160524j20160531 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHigher-Dimensional Generalized Manifolds: Surgery and Constructions$b[electronic resource] /$fAlberto Cavicchioli, Friedrich Hegenbarth, Dus?an D. Repovs? 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016 215 $a1 online resource (154 pages) 225 0 $aEMS Series of Lectures in Mathematics (ELM) ;$x2523-5176 311 $a3-03719-156-2 327 $aGeneralized manifolds: introduction -- Surgery theory and applications to resolutions of generalized manifolds -- Controlled surgery theory and constructions of generalized manifolds -- Generalized manifolds and surgery theory. 330 $aGeneralized 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. 517 $aHigher-Dimensional Generalized Manifolds 606 $aTopology$2bicssc 606 $aManifolds and cell complexes$2msc 606 $aCategory theory; homological algebra$2msc 606 $a$K$-theory$2msc 615 07$aTopology 615 07$aManifolds and cell complexes 615 07$aCategory theory; homological algebra 615 07$a$K$-theory 676 $a516.07 686 $a57-xx$a18-xx$a19-xx$2msc 700 $aCavicchioli$b Alberto$0149559 702 $aHegenbarth$b Friedrich 702 $aRepovs?$b Dus?an D. 801 0$bch0018173 906 $aBOOK 912 $a9910153273303321 996 $aHigher-Dimensional Generalized Manifolds: Surgery and Constructions$92564811 997 $aUNINA